Deck 5: Applications of Linear Equations

Question 1

Determine the slope and y-intercept of each of the following equations:
-2x = 3y + 4

Answer 1

slope = ; intercept =

Question 2

Determine the slope and y-intercept of each of the following equations:
-8 - 3x = 2y

Answer 2

b) slope = ; intercept = 4

Question 3

Determine the slope and y-intercept of each of the following equations:
-8x - 2y - 3 = 0

Answer 3

slope = 4; intercept =

Question 4

Determine the slope and y-intercept of each of the following equations:
-6x = 9y

Question 5

Determine the slope and y-intercept of each of the following equations:
-2b + 3 = 5a

Question 6

Determine the slope and y-intercept of each of the following equations:
-3a - 4b = 12

Question 7

Determine the slope and y-intercept of each of the following equations:
-0 = 2400 - 4a - 5b

Question 8

Determine the slope and y-intercept of each of the following equations:
-7a = -89b

Question 9

A plumber charges a flat $50 for a home service call plus $10 per 15 minutes of labour. Write an equation for calculating the total charges, C, in terms of the hours of labour, H. If you were to plot a graph of C vs. H, what would be the slope and C-intercept of the line?

Question 10

The formula for converting from Celsius temperatures, C, to Fahrenheit temperatures, F, is F = C + 32.
a) If you were to plot a graph of F vs. C, what would be the slope and F-intercept of the line?
b) The slope represents the change in F per unit change in C. Use the value of the slope to determine the increase in Fahrenheit temperature corresponding to a 10 Celsius-degree rise.
c) Rearrange the given formula to obtain a formula for converting from Fahrenheit temperatures to Celsius temperatures. What would be the slope and C-intercept if C vs. F were plotted on a graph?

Question 11

Use the graphical method to solve the following pair of equations.

Question 12

Use the graphical method to solve the following pair of equations.

Question 13

Use the graphical method to solve the following pair of equations.

Question 14

the graphical method to solve the following pair of equations.

Question 15

Use the graphical method to solve the following pair of equations.

Question 16

Use the graphical method to solve the following pair of equations.

Question 17

the graphical method to solve the following pair of equations.

Question 18

Use the graphical method to solve the following pair of equations.

Question 19

Dynacan Ltd. manufactured 10,000 units of product last year and identified the following manufacturing and overhead costs. (V denotes "variable cost" and F denotes "fixed cost.") If unit variable costs and fixed costs remain unchanged, calculate the total cost to produce 9700 units this year.

Question 20

CD Solutions Ltd. manufactures and replicates CDs for software and music recording companies. CD Solutions sells each disc for $2.50. The variable costs per disc are $1.00.
a) To just break even, how many CDs must be sold per month if the fixed costs are $60,000 per month?
b) What must sales be in order to have a profit of $7500 per month?

Question 21

Clone Computers assembles and packages personal computer systems from brand-name components. Its Home Office PC System is assembled from components costing $1400 per system and sells for $2000. Labour costs for assembly are $100 per system. This product line's share of overhead costs is $10,000 per month.
a) How many Home Office Systems must be sold each month to break even on this product line?
b) What will be the profit or loss for a month in which 15 Home Office Systems are sold?

Question 22

Alpha Corp. expects to operate at 80% of capacity next year. Its forecast operating budget is:

a) What is Alpha's break-even revenue?
b) What would be Alpha's net income if it operates at full capacity?

Question 23

Beta Inc. has based its budget forecast for next year on the assumption it will operate at 90% of capacity. The budget is
a) At what percentage of capacity would Beta break even?
b) What would be Beta's net income if it operates at 70% of capacity?

Question 24

Bentley Plastics Ltd. has annual fixed costs of $450,000 and variable costs of $15 per unit. The selling price per unit is $25.
a) What annual revenue is required to break even?
b) What annual unit sales are required to break even?
c) What will be the annual net income at annual sales of: (i) 50,000 units? (ii) $1,000,000?
d) What minimum annual unit sales are required to limit the annual loss to $20,000?
e) If the unit selling price and fixed costs remain the same, what are the changes in break-even unit sales and break-even revenue for a $1 increase in variable costs?

Question 25

The Morgan Company produces two products, G and H, with the following characteristics: Total fixed costs for the year are expected to be $700,000.

a) What will be the net income if the forecast sales are realized?
b) Determine the break-even volumes of the two products. Assume that the product mix (that is, the ratio of the unit sales for the two products) remains the same at the break-even point.
c) If it turns out that Morgan sells twice as many units of H as of G, what will be the break-even volumes of the two products?

Question 26

Genifax reported the following information for September: a) Determine the unit sales required to break even.
b) What unit sales would generate a net income of $30,000?
c) What unit sales would generate a profit of 20% of the sales dollars?
d) What sales dollars are required to produce a profit of $20,000?
e) If unit variable costs are reduced by 10% with no change in the fixed costs, what will the break-even point become?

Question 27

The social committee of a college's student government is planning the annual graduation dinner and dance. The preferred band can be signed for $1000 plus 10% of ticket revenues. A hall can be rented for $4400. Fire regulations limit the hall to 400 guests plus the band and caterers. A food caterer has quoted a price of $24 per person for the dinner. The committee thinks that the event will be a sellout if ticket prices are set at $46 per person. Some on the committee are in favour of less crowding at the dance and argue for a ticket price of $56. They estimate that 300 will attend at the higher price.
a) Calculate the number of tickets that need to be sold at each price to break even.
b) What will the profit be at the predicted sales at each ticket price?

Question 28

This problem is designed to illustrate how the relative proportions of fixed and variable costs affect a firm's net income when the sales volume changes. Two hypothetical firms, A and B, manufacture and sell the same product at the same price of $50. Firm A is highly mechanized with monthly fixed costs of $4000 and unit variable costs of $10. Firm B is labour-intensive and can readily lay off or take on more workers as production requirements warrant. B's monthly fixed costs are $1000, and its unit variable costs are $40.
a) Calculate the break-even volume for both firms.
b) At each firm's break-even point, calculate the proportion of the firm's total costs that are fixed and the proportion that are variable.
c) For a 10% increase in sales above the break-even point, calculate the dollar increase in each firm's net income. Explain the differing results.
d) For a 10% decrease in sales below the break-even point, calculate the dollar decrease in each firm's net income. Explain the differing results.
e) What is each firm's net income at sales of 150 units per month and each firm's loss at sales of 50 units per month?

Question 29

A farmer is trying to decide whether to rent his neighbour's land to grow additional hay for sale to feedlots at $180 per delivered tonne. The land can be rented at $400 per hectare for the season. Cultivation and planting will cost $600 per hectare; spraying and fertilizer will cost $450 per hectare. It will cost $42 per tonne to cut, condition, and bale the hay, and $24 per tonne to transport it to the feedlots.
a) How many tonnes per hectare must be produced to break even?
b) How much is the break-even tonnage lowered if the selling price is $10 per tonne higher?
c) What is the profit or loss at the $180 per tonne price if the crop yield is: (i) 15 tonnes per hectare? (ii) 10 tonnes per hectare?

Question 30

Use the graphical approach to CVP analysis to solve the following problem.
CD Solutions Ltd. manufactures and replicates CDs for software and music recording companies. CD Solutions sells each disc for $2.50. The variable costs per disc are $1.00.
a) To just break even, how many CDs must be sold per month if the fixed costs are $60,000 per month?
b) What must sales be in order to have a profit of $7500 per month?

Question 31

Use the graphical approach to CVP analysis to solve the following problem.
Clone Computers assembles and packages personal computer systems from brand-name components. Its Home Office PC System is assembled from components costing $1400 per system and sells for $2000. Labour costs for assembly are $100 per system. This product line's share of overhead costs is $10,000 per month.
a) How many Home Office Systems must be sold each month to break even on this product line?
b) What will be the profit or loss for a month in which 15 Home Office Systems are sold?

Question 32

Use the Interactive break-even Chart in the textbook's OLC to answer the following problem. To access the chart, follow the instructions given in the NET @ssets box at the beginning of section 5.4 in the text. Leaving other variables unchanged, what effect does increasing the value of VC have on:
a. The Fixed Cost (FC) line?
b. The Total Cost (TC) line?
c. The Total Revenue (TR) line?
d. The break-even point?

Question 33

Use the Interactive break-even Chart in the textbook's OLC to answer the following problem. To access the chart, follow the instructions given in the NET @ssets box at the beginning of section 5.4 in the text. Leaving other variables unchanged, what effect does increasing the value of S have on:
a. The Fixed Cost (FC) line?
b. The Total Cost (TC) line?
c. The Total Revenue (TR) line?
d. The break-even point?

Question 34

Use the Interactive break-even Chart in the textbook's OLC to answer the following problem. To access the chart, follow the instructions given in the NET @ssets box at the beginning of section 5.4 in the text. Leaving other variables unchanged, what effect does increasing the value of FC have on:
a. The Fixed Cost (FC) line?
b. The Total Cost (TC) line?
c. The Total Revenue (TR) line?
d. The break-even point?

Question 35

Use the Interactive break-even Chart and its accompanying in the textbook's OLC to answer the following problem. To access the chart, follow the instructions given in the NET @ssets box at the beginning of section 5.4 in the text.
Clone Computers assembles and packages personal computer systems from brand-name components. Its Home Office PC System is assembled from components costing $1400 per system and sells for $2000. Labour costs for assembly are $100 per system. This product line's share of overhead costs is $10,000 per month.
a) How many Home Office Systems must be sold each month to break even on this product line?
b) What will be the profit or loss for a month in which 15 Home Office Systems are sold?

Question 36

Use the Interactive break-even Chart and its accompanying in the textbook's OLC to answer the following problem. To access the chart, follow the instructions given in the NET @ssets box at the beginning of section 5.4 in the text.
Huntsville Office Supplies (HOS) is evaluating the profitability of leasing a photocopier for its customers to use on a self-serve basis at 10′ per copy. The copier may be leased for $300 per month plus 1.5′ per copy on a full-service contract. HOS can purchase paper at $5 per 500-sheet ream. Toner costs $100 per bottle, which in normal use will last for 5000 pages. HOS is allowing for additional costs (including electricity) of 0.5′ per copy.
a) How many copies per month must be sold in order to break even?
b) What will be the increase in monthly profit for each 1000 copies sold above the break-even point?

Question 37

Use the Interactive break-even Chart and its accompanying in the textbook's OLC to answer the following problem. To access the chart, follow the instructions given in the NET @ssets box at the beginning of section 5.4 in the text.
Jordan is developing a business plan for a residential building inspection service he may start. Rent and utilities for an office would cost $1000 per month. The fixed costs for a vehicle would be $450 per month. He estimates that the variable office costs (word processing and supplies) will be $50 per inspection and variable vehicle costs will be $25 per inspection. Jordan would also spend $200 per month to lease a computer, and $350 per month for advertising.
a) If he charges $275 per inspection, how many inspections per month are required before he can "pay himself?"
b) How many inspections per month are required for Jordan to be able to draw a salary of $4000 per month?

Question 38

Solve the following problem using the Contribution Margin Approach.
Reliable Plastics makes containers that it sells for $2.55 each. Its fixed costs for this product are $2000 per month and the variable cost per unit is $1.30.
a) What is the break-even point in units?
b) What is the break-even sales revenue?

Question 39

Solve the following problem using the Contribution Margin Approach.
CD Solutions Ltd. manufactures and replicates CDs for software and music recording companies. CD Solutions sells each disc for $2.50. The variable costs per disc are $1.00.
a) To just break even, how many CDs must be sold per month if the fixed costs are $60,000 per month?
b) What must sales be in order to have a profit of $7500 per month?

Question 40

Solve the following problem using the Contribution Margin Approach.
Clone Computers assembles and packages personal computer systems from brand-name components. Its Home Office PC System is assembled from components costing $1400 per system and sells for $2000. Labour costs for assembly are $100 per system. This product line's share of overhead costs is $10,000 per month.
a) How many Home Office Systems must be sold each month to break even on this product line?
b) What will be the profit or loss for a month in which 15 Home Office Systems are sold?

Question 41

Solve the following problem using the Contribution Margin Approach.
Huntsville Office Supplies (HOS) is evaluating the profitability of leasing a photocopier for its customers to use on a self-serve basis at 10′ per copy. The copier may be leased for $300 per month plus 1.5′ per copy on a full-service contract. HOS can purchase paper at $5 per 500-sheet ream. Toner costs $100 per bottle, which in normal use will last for 5000 pages. HOS is allowing for additional costs (including electricity) of 0.5′ per copy.
a) How many copies per month must be sold in order to break even?
b) What will be the increase in monthly profit for each 1000 copies sold above the break-even point?

Question 42

Solve the following problem using the Contribution Margin Approach.
Jordan is developing a business plan for a residential building inspection service he may start. Rent and utilities for an office would cost $1000 per month. The fixed costs for a vehicle would be $450 per month. He estimates that the variable office costs (word processing and supplies) will be $50 per inspection and variable vehicle costs will be $25 per inspection. Jordan would also spend $200 per month to lease a computer, and $350 per month for advertising.
a) If he charges $275 per inspection, how many inspections per month are required before he can "pay himself?"
b) How many inspections per month are required for Jordan to be able to draw a salary of $4000 per month?

Question 43

Solve the following problem using the Contribution Margin Approach.
Alpha Corp. expects to operate at 80% of capacity next year. Its forecast operating budget is:
a) What is Alpha's break-even revenue?
b) What would be Alpha's net income if it operates at full capacity?

Question 44

Solve the following problem using the Contribution Margin Approach.
Beta Inc. has based its budget forecast for next year on the assumption it will operate at 90% of capacity. The budget is
a) At what percentage of capacity would Beta break even?
b) What would be Beta's net income if it operates at 70% of capacity?

Question 45

Solve the following problem using the Contribution Margin Approach.
Valley Peat Ltd. sells peat moss for $10 per bag. Variable costs are $7.50 per bag and annual fixed costs are $100,000.
a) How many bags of peat must be sold to break even?
b) What will be the net income for a year in which 60,000 bags of peat are sold?
c) How many bags must be sold for a net income of $60,000 in a year?
d) What annual sales in terms of bags and in terms of dollars would produce a loss of $10,000?
e) How much do the break-even unit sales and break-even revenue increase per $1000 increase in annual fixed costs?

Question 46

Solve the following problem using the Contribution Margin Approach.
Reflex Manufacturing Corp. manufactures composters at a unit variable cost of $43. It sells them for $70 each. It can produce a maximum of 3200 composters per month. Annual fixed costs total $648,000.
a) What is the break-even volume per month?
b) What is the monthly net income at a volume of 2500 composters per month?
c) What is the monthly net income if Reflex operates at 50% of capacity during a recession?
d) At what percent utilization would the annual net income be $226,800?
e) If fixed and variable costs remain the same, how much do the monthly break-even unit sales change for a $1 increase in the selling price?

Question 47

Solve the following problem using the Contribution Margin Approach.
Bentley Plastics Ltd. has annual fixed costs of $450,000 and variable costs of $15 per unit. The selling price per unit is $25.
a) What annual revenue is required to break even?
b) What annual unit sales are required to break even?
c) What will be the annual net income at annual sales of: (i) 50,000 units? (ii) $1,000,000?
d) What minimum annual unit sales are required to limit the annual loss to $20,000?
e) If the unit selling price and fixed costs remain the same, what are the changes in break-even unit sales and break-even revenue for a $1 increase in variable costs?

Question 48

Solve the following problem using the Contribution Margin Approach.
The Woodstock plant of Goodstone Tires manufactures a single line of automobile tires. In its first fiscal quarter, the plant had total revenue of $4,500,000 and net income of $900,000 from the production and sale of 60,000 tires. In the subsequent quarter, the net income was $700,000 from the production and sale of 50,000 tires. Calculate the unit selling price, the total revenue in the second quarter, the variable costs per tire, and the total fixed costs per calendar quarter.

Question 49

Solve the following problem using the Contribution Margin Approach.
The Kelowna division of Windstream RVs builds the Wanderer model. The division had total revenue of $4,785,000 and a profit of $520,000 on the sale of 165 units in the first half of its financial year. Sales declined to 117 units in the second half of the year, resulting in a profit of only $136,000. Determine the selling price per unit, the total revenue in the second half, the unit variable costs, and the annual fixed costs.

Question 50

Solve the following problem using the Contribution Margin Approach.
In the past year, the Greenwood Corporation had sales of $1,200,000, fixed costs of $400,000, and total variable costs of $600,000.
a) At what sales figure would Greenwood have broken even last year?
b) If sales increase by 15% in the year ahead (but all prices remain the same), how much (in $) will the net income increase?
c) If fixed costs are 10% lower in the year ahead (but sales and variable costs remain the same as last year), how much (in $) will the net income increase?
d) If variable costs are 10% higher in the year ahead (but sales and fixed costs remain the same as last year), how much (in $) will the net income decrease?

Question 51

Solve the following problem using the Contribution Margin Approach.
The Morgan Company produces two products, G and H, with the following characteristics:
Total fixed costs for the year are expected to be $700,000.
a) What will be the net income if the forecast sales are realized?
b) Determine the break-even volumes of the two products. Assume that the product mix (that is, the ratio of the unit sales for the two products) remains the same at the break-even point.
c) If it turns out that Morgan sells twice as many units of H as of G, what will be the break-even volumes of the two products?

Question 52

Solve the following problem using the Contribution Margin Approach.
A college ski club is planning a weekend package for its members. The members will each be charged $270. For a group of 15 or more, the club can purchase a 2-day downhill pass and 2 nights' accommodation for $220 per person. A 36-passenger capacity bus can be chartered for $1400.
a) How many must sign up for the package for all costs to be covered?
b) If the bus is filled, how much profit will the club make?
c) If the student government agrees to cover any loss up to $400, what is the minimum number of participants required?

Question 53

Solve the following problem using the Contribution Margin Approach.
Genifax reported the following information for September: a) Determine the unit sales required to break even.
b) What unit sales would generate a net income of $30,000?
c) What unit sales would generate a profit of 20% of the sales dollars?
d) What sales dollars are required to produce a profit of $20,000?
e) If unit variable costs are reduced by 10% with no change in the fixed costs, what will the break-even point become?

Question 54

Solve the following problem using the Contribution Margin Approach.
The social committee of a college's student government is planning the annual graduation dinner and dance. The preferred band can be signed for $1000 plus 10% of ticket revenues. A hall can be rented for $4400. Fire regulations limit the hall to 400 guests plus the band and caterers. A food caterer has quoted a price of $24 per person for the dinner.
The committee thinks that the event will be a sellout if ticket prices are set at $46 per person. Some on the committee are in favour of less crowding at the dance and argue for a ticket price of $56. They estimate that 300 will attend at the higher price.
a) Calculate the number of tickets that need to be sold at each price to break even.
b) What will the profit be at the predicted sales at each ticket price?

Question 55

Solve the following problem using the Contribution Margin Approach.
This problem is designed to illustrate how the relative proportions of fixed and variable costs affect a firm's net income when the sales volume changes.
Two hypothetical firms, A and B, manufacture and sell the same product at the same price of $50. Firm A is highly mechanized with monthly fixed costs of $4000 and unit variable costs of $10. Firm B is labour-intensive and can readily lay off or take on more workers as production requirements warrant. B's monthly fixed costs are $1000, and its unit variable costs are $40.
a) Calculate the break-even volume for both firms.
b) At each firm's break-even point, calculate the proportion of the firm's total costs that are fixed and the proportion that are variable.
c) For a 10% increase in sales above the break-even point, calculate the dollar increase in each firm's net income. Explain the differing results.
d) For a 10% decrease in sales below the break-even point, calculate the dollar decrease in each firm's net income. Explain the differing results.
e) What is each firm's net income at sales of 150 units per month and each firm's loss at sales of 50 units per month?

Question 56

Solve the following problem using the Contribution Margin Approach.
In the year just ended, a small appliance manufacturer sold its griddle at the wholesale price of $37.50. The unit variable costs were $13.25, and the monthly fixed costs were $5600.
a) If unit variable costs are expected to rise to $15.00 and fixed costs to $6000 per month for the next year, at what amount should the griddle be priced in order to have the same break-even volume as last year?
b) What should be the griddle's price in order to have the same profit as last year on sales of 300 griddles per month in both years?

Question 57

Solve the following problem using the Contribution Margin Approach.
Mickey's Restaurant had a net income last year of $40,000 after fixed costs of $130,000 and total variable costs of $80,000.
a) What was the restaurant's break-even point in sales dollars?
b) If fixed costs in the current year rise to $140,000 and variable costs remain at the same percentage of sales as for last year, what will be the break-even point?

Question 58

Solve the following problem using the Contribution Margin Approach.
A farmer is trying to decide whether to rent his neighbour's land to grow additional hay for sale to feedlots at $180 per delivered tonne. The land can be rented at $400 per hectare for the season. Cultivation and planting will cost $600 per hectare; spraying and fertilizer will cost $450 per hectare. It will cost $42 per tonne to cut, condition, and bale the hay, and $24 per tonne to transport it to the feedlots.
a) How many tonnes per hectare must be produced to break even?
b) How much is the break-even tonnage lowered if the selling price is $10 per tonne higher?
c) What is the profit or loss at the $180 per tonne price if the crop yield is:
(i) 15 tonnes per hectare? (ii) 10 tonnes per hectare?

Question 59

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem:
Ingrid processes and bottles jam in her home-based business. Her fixed costs are $250 per month and the variable cost per jar is $1.20. She sells the jam to local grocery stores for $3.20 each.
a) How many jars must she sell per year to break even?
b) What will be her profit if she sells 3000 jars in a year?

Question 60

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In
the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5,
select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart
to solve the following problem:
ChildCare Industries manufactures infant car seats that it sells to retailers for $155 each. The costs to
manufacture each additional seat are $65, and the monthly fixed costs are $18,000.
a) How many seats must be sold per year to break even?
b) What will ChildCare's loss be if it sells 2000 seats in a year?

Question 61

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem:
ChildCare Industries manufactures infant car seats that it sells to retailers for $155 each. The costs to manufacture each additional seat are $65, and the monthly fixed costs are $18,000.
a) To just break even, how many CDs must be sold per month if the fixed costs are $60,000 per month?
b) What must sales be in order to have a profit of $7500 per month?

Question 62

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem:
Clone Computers assembles and packages personal computer systems from brand-name components. Its Home Office PC System is assembled from components costing $1400 per system and sells for $2000. Labour costs for assembly are $100 per system. This product line's share of overhead costs is $10,000 per month.
a) How many Home Office Systems must be sold each month to break even on this product line?
b) What will be the profit or loss for a month in which 15 Home Office Systems are sold?

Question 63

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem:
Huntsville Office Supplies (HOS) is evaluating the profitability of leasing a photocopier for its customers to use on a self-serve basis at 10′ per copy. The copier may be leased for $300 per month plus 1.5′ per copy on a full-service contract. HOS can purchase paper at $5 per 500-sheet ream. Toner costs $100 per bottle, which in normal use will last for 5000 pages. HOS is allowing for additional costs (including electricity) of 0.5′ per copy
a) How many copies per month must be sold in order to break even?
b) What will be the increase in monthly profit for each 1000 copies sold above the break-even point?

Question 64

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem:
Jordan is developing a business plan for a residential building inspection service he may start. Rent and utilities for an office would cost $1000 per month. The fixed costs for a vehicle would be $450 per month. He estimates that the variable office costs (word processing and supplies) will be $50 per inspection and variable vehicle costs will be $25 per inspection. Jordan would also spend $200 per month to lease a computer, and $350 per month for advertising.
a) If he charges $275 per inspection, how many inspections per month are required before he can "pay himself?"
b) How many inspections per month are required for Jordan to be able to draw a salary of $4000 per month?

Question 65

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem:
A small manufacturing operation can produce up to 250 units per week of a product that it sells for $20 per unit. The variable cost per unit is $12, and the fixed cost per week is $1200.
a) How many units must it sell per week to break even?
b) Determine the firm's weekly profit or loss if it sells: (i) 120 units per week (ii) 250 units per week
c) At what level of sales will the net income be $400 per week?

Question 66

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem:
Valley Peat Ltd. sells peat moss for $10 per bag. Variable costs are $7.50 per bag and annual fixed costs are $100,000.
a) How many bags of peat must be sold to break even?
b) What will be the net income for a year in which 60,000 bags of peat are sold?
c) How many bags must be sold for a net income of $60,000 in a year?
d) What annual sales in terms of bags and in terms of dollars would produce a loss of $10,000?
e) How much do the break-even unit sales and break-even revenue increase per $1000 increase in annual fixed costs?

Question 67

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem:
Reflex Manufacturing Corp. manufactures composters at a unit variable cost of $43. It sells them for $70 each. It can produce a maximum of 3200 composters per month. Annual fixed costs total $648,000.
a) What is the break-even volume per month?
b) What is the monthly net income at a volume of 2500 composters per month?
c) What is the monthly net income if Reflex operates at 50% of capacity during a recession?
d) At what percent utilization would the annual net income be $226,800?
e) If fixed and variable costs remain the same, how much do the monthly break-even unit sales change for a $1 increase in the selling price?

Question 68

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem:
Bentley Plastics Ltd. has annual fixed costs of $450,000 and variable costs of $15 per unit. The selling price per unit is $25.
a) What annual revenue is required to break even?
b) What annual unit sales are required to break even?
c) What will be the annual net income at annual sales of: (i) 50,000 units? (ii) $1,000,000?
d) What minimum annual unit sales are required to limit the annual loss to $20,000?
e) If the unit selling price and fixed costs remain the same, what are the changes in break-even unit sales and break-even revenue for a $1 increase in variable costs?

Question 69

The Armour Company had the following revenue and costs in the most recently completed fiscal year:
a) What is the unit sales volume at the break-even point?
b) How many units must be produced and sold for the company to have a net income of $1,000,000 for the year?

Question 70

During an economic slowdown, an automobile plant lost $12,000,000 on the production and sale of 9000 cars. Total revenue for the year was $270,000,000. If the break-even volume for the plant is 10,000 cars per year, calculate:
a) The plant's total fixed costs for a year.
b) The net income if unit sales for the year had been equal to the 5-year average of 12,000.

Question 71

The monthly fixed costs of operating a 30-unit motel are $14,000. The price per unit per night for next year is set at $55. Costs arising from rentals on a per-unit per-day basis are $6 for maid service, $3 for supplies and laundry, and $3 for heat and utilities.
a) Based on a 30-day month, at what average occupancy rate will the motel break even?
b) What will the motel's net income be at an occupancy rate of: (i) 40%? (ii) 30%?
c) Should the owner reduce the price from $55 to $47 per unit per night if it will result in an increase in the average occupancy rate from 40% to 50%? Present calculations that justify your answer.

Question 72

Solve the following set of equations graphically:

Question 73

Solve the following set of equations graphically:

Question 74

Solve the following set of equations graphically:

Question 75

Solve the following set of equations graphically:

Question 76

Solve the following set of equations graphically:

Question 77

Solve the following set of equations graphically:

Question 78

Solve the following set of equations graphically:

Question 79

M Studios estimates that it can sell 1500 camera lenses at $150 each. Total fixed costs are $120,000, and variable costs are $30 per lens. What unit sales are required to break even? What is the revenue generated if all units are sold? Use the graphical approach to CVP analysis to solve.

Question 80

A company expects to sell 30,000 hats at $35 each. The estimated variable cost of each hat is $12.50, and the fixed costs are estimated to be $450,000. Calculate the breakeven point in units and revenue. Use the graphical approach to CVP analysis to solve.