Deck 25: The Application of Linear Programming to Management Accounting

Question 1

Figure 25-2
Heft Company produces A and B with contribution margins per unit of £40 and £30, respectively. Only 500 labour hours and 300 machine hours are available for production.
Time requirements to produce one unit of A and B are as follows: $\begin{array}{cc}&\text { Product A } & \text { Product B } \\\text { Labour hours per unit }&5 & 2 \\\text { Machine hours per unit }&1 & 4\end{array}$

-Refer to Figure 25-2. What is the objective function to maximize profits for Heft Company?

A)Minimize 5A + 2B
B)Maximize 1A + 4B
C)Maximize 40A + 30B
D)Minimize 40A + 30B

Answer 1

Maximize 40A + 30B

Question 2

A linear programming problem has the following objective function: 20X + 40Y + 60Z. If the optimal solution provided by the model is to produce and sell 100, 200 and 300 units of X, Y, and Z, respectively, what is the expected return?

A)£36,000
B)£28,000
C)£120
D)£24,000

Answer 2

B

Question 3

Figure 25-2
Heft Company produces A and B with contribution margins per unit of £40 and £30, respectively. Only 500 labour hours and 300 machine hours are available for production.
Time requirements to produce one unit of A and B are as follows: $\begin{array}{cc}&\text { Product A } & \text { Product B } \\\text { Labour hours per unit }&5 & 2 \\\text { Machine hours per unit }&1 & 4\end{array}$

-Refer to Figure 25-2. What is the constraint on machine hours for Heft Company?

A)1A + 4B $\le$ 500
B)5A + 2B $\le$ 500
C)1A + 4B $\le$ 300
D)40A + 30B $\le$ 500

Answer 3

1A + 4B $\le$ 300

Question 4

A linear programming model would NOT include which of the following items?

A)independent variables
B)networks
C)dependent variables
D)objective function

Question 5

Figure 25-1
Hassel Company manufactures two different products, X and Y. The company has 100 kgs of materials and 300 direct labour hours available for production.
The time requirements and contribution margins per unit are as follows: $\begin{array}{lrr}&\text { Product X }&\text { Product Y }\\\text { Contribution margin per unit } & £ 4 & £ 5 \\\text { Materials per unit (lbs.) } & 1 & 2 \\\text { Direct labour hours per unit } & 4 & 2\end{array}$

-Refer to Figure 25-1. What is the equation for the constraint on direct labour?

A)£1X + £2Y $\le$ 300
B)£4X + £2Y $\le$ 100
C)£4X + £5Y $\le$ 100
D)£4X + £2Y $\le$ 300

Question 6

Using the graphic approach to linear programming, the solution is usually

A)a corner point where two or more constraints intersect.
B)where the lines intersect farthest from zero.
C)the point farthest from the Y-axis.
D)the point farthest from the X-axis.

Question 7

Figure 25-6
Anderson Company manufactures two different products: A and B. The company has 100 kgs of raw materials and 300 direct labour-hours available for production.
The time requirements and contribution margins per unit are as follows: $\begin{array}{lcr}&A&B\\\text { Raw materials per unit (lbs.) } & 1 & 2 \\\text { Direct-labour hours per unit } & 4 & 2 \\\text { Contribution margin per unit } & E 4 & E 5\end{array}$

-Refer to Figure 25-6. What is the objective function for Anderson Company?

A)Minimize £4A + £5B.
B)Maximize £4A + £5B.
C)Maximize £1A + £2B.
D)Maximize £4A + £2B.

Question 8

Figure 25-1
Hassel Company manufactures two different products, X and Y. The company has 100 kgs of materials and 300 direct labour hours available for production.
The time requirements and contribution margins per unit are as follows: $\begin{array}{lrr}&\text { Product X }&\text { Product Y }\\\text { Contribution margin per unit } & £ 4 & £ 5 \\\text { Materials per unit (lbs.) } & 1 & 2 \\\text { Direct labour hours per unit } & 4 & 2\end{array}$

-Refer to Figure 25-1. What is the objective function for maximizing profits?

A)Minimize £4X + £5Y
B)Maximize £4X + £5Y
C)Maximize £1X + £2Y
D)Maximize £4X + £2Y

Question 9

Figure 25-4
The following information is available for Wilson Trailer Company, which sells two products: $$\begin{array} { l c c } & \text { Trailer A } & \text { Trailer B } \\\text { Processing time } & 2 \text { hours } & 4 \text { hours } \\\text { Vinyl cover used } & 16 \text { sq. ft. } & 12 \text { sq. ft. } \\\text { Selling price } & £ 50.00 & £ 80.00 \\\text { Variable cost } & £ 35.00 & £ 50.00 \\\text { Fixed cost } & £ 10.00 & £ 20.00\end{array}$$ There are 100 hours available in the plant and 75 square metres of vinyl available per operating period.

-Refer to Figure 25-4. The constraint equation representing the materials available for the production processes is

A)2A + 4B $\ge$ 100.
B)16A + 12B = 75.
C)2A + 4B = 200.
D)16A + 12B $\le$ 75.

Question 10

A linear programming problem has an objective function of 10X + 12Y. If the optimal solution provided by the model is to produce and sell 400 units of X and 1,000 units of Y, the expected return is

A)£1,400.
B)£40,800.
C)£14,800.
D)£16,000.

Question 11

Figure 25-5
The following information is available for Walters Furniture Company, which sells two products: $\begin{array}{lcc} & \text { Table X } & \text { Table Y } \\\text { Processing time } & 4 \text { hours } & 6 \text { hours } \\\text { Metal used } & 30 \mathrm{sq} . \mathrm{ft} . & 18 \mathrm{sq} . \mathrm{ft} . \\\text { Selling price } & £ 200.00 & £ 100.00 \\\text { Variable cost } & £ 150.00 & £ 60.00 \\\text { Fixed cost } & £ 30.00 & £ 30.00\end{array}$ There are 200 hours available in the plant and 200 square metres of metal available per operating period.

-Refer to Figure 25-5. What is the objective function for maximizing sales?

A)Maximize 200X + 100Y
B)Maximize 180X + 90Y
C)Maximize 50X + 40Y
D)Minimize 200X + 100Y

Question 12

In the graphic method of solving a linear programming problem, which of the following is depicted on the graph?

A)coefficient of correlation
B)constraint
C)least-squares line of best fit
D)break-even point

Question 13

Figure 25-3
Tiffany Manufacturing Company produces X and Y with contribution margins per unit of £10 and £90, respectively. Only 200 labour hours and 400 machine hours are available for production.
Time requirements to produce one unit of X and Y are as follows: $\begin{array}{cc}&\text { Product A } & \text { Product B } \\\text { Labour hours per unit }&1&2 \\\text { Machine hours per unit }&5&1\end{array}$

-Refer to Figure 25-3. What is the constraint on machine hours for Tiffany Manufacturing Company?

A)10X + 90Y $\le$ 200
B)1X + 2Y $\le$ 400
C)1X + 2Y $\le$ 200
D)5X + 1Y $\le$ 400

Question 14

Figure 25-3
Tiffany Manufacturing Company produces X and Y with contribution margins per unit of £10 and £90, respectively. Only 200 labour hours and 400 machine hours are available for production.
Time requirements to produce one unit of X and Y are as follows: $\begin{array}{cc}&\text { Product A } & \text { Product B } \\\text { Labour hours per unit }&1&2 \\\text { Machine hours per unit }&5&1\end{array}$

-Refer to Figure 25-3. What is the objective function to maximize profits for Tiffany Manufacturing Company?

A)Minimize 10X + 90Y
B)Maximize 1X + 2Y
C)Maximize 10X + 90Y
D)Minimize 1X + 2Y

Question 15

Figure 25-4
The following information is available for Wilson Trailer Company, which sells two products: $$\begin{array} { l c c } & \text { Trailer A } & \text { Trailer B } \\\text { Processing time } & 2 \text { hours } & 4 \text { hours } \\\text { Vinyl cover used } & 16 \text { sq. ft. } & 12 \text { sq. ft. } \\\text { Selling price } & £ 50.00 & £ 80.00 \\\text { Variable cost } & £ 35.00 & £ 50.00 \\\text { Fixed cost } & £ 10.00 & £ 20.00\end{array}$$ There are 100 hours available in the plant and 75 square metres of vinyl available per operating period.

-Refer to Figure 25-4. What is the objective function for maximizing profits?

A)Maximize £15A + £30B
B)Maximize £50A + £80B
C)Maximize £35A + £50B
D)Minimize £15A + £30B

Question 16

Figure 25-4
The following information is available for Wilson Trailer Company, which sells two products: $$\begin{array} { l c c } & \text { Trailer A } & \text { Trailer B } \\\text { Processing time } & 2 \text { hours } & 4 \text { hours } \\\text { Vinyl cover used } & 16 \text { sq. ft. } & 12 \text { sq. ft. } \\\text { Selling price } & £ 50.00 & £ 80.00 \\\text { Variable cost } & £ 35.00 & £ 50.00 \\\text { Fixed cost } & £ 10.00 & £ 20.00\end{array}$$ There are 100 hours available in the plant and 75 square metres of vinyl available per operating period.

-Refer to Figure 25-4. Which of the following statements is INCORRECT?

A)The materials constraint favours Trailer B over Trailer A.
B)The time constraint favours Trailer A over Trailer B.
C)The material constraint favours Trailer A over Trailer B.
D)The objective function favours Trailer B over Trailer A.

Question 17

Figure 25-2
Heft Company produces A and B with contribution margins per unit of £40 and £30, respectively. Only 500 labour hours and 300 machine hours are available for production.
Time requirements to produce one unit of A and B are as follows: $\begin{array}{cc}&\text { Product A } & \text { Product B } \\\text { Labour hours per unit }&5 & 2 \\\text { Machine hours per unit }&1 & 4\end{array}$

-Refer to Figure 25-2. What is the constraint on labour hours for Heft Company?

A)5A + 1B $\le$ 500
B)5A + 2B $\le$ 500
C)1A + 4B $\le$ 300
D)40A + 30B $\le$ 500

Question 18

Figure 25-5
The following information is available for Walters Furniture Company, which sells two products: $\begin{array}{lcc} & \text { Table X } & \text { Table Y } \\\text { Processing time } & 4 \text { hours } & 6 \text { hours } \\\text { Metal used } & 30 \mathrm{sq} . \mathrm{ft} . & 18 \mathrm{sq} . \mathrm{ft} . \\\text { Selling price } & £ 200.00 & £ 100.00 \\\text { Variable cost } & £ 150.00 & £ 60.00 \\\text { Fixed cost } & £ 30.00 & £ 30.00\end{array}$ There are 200 hours available in the plant and 200 square metres of metal available per operating period.

-Refer to Figure 25-5. The constraint equation representing processing time available is

A)4X + 6Y $\ge$ 200.
B)4X + 6Y $\le$ 200.
C)30X + 18Y $\le$ 200.
D)4X + 6Y $\le$ 400.

Question 19

Figure 25-3
Tiffany Manufacturing Company produces X and Y with contribution margins per unit of £10 and £90, respectively. Only 200 labour hours and 400 machine hours are available for production.
Time requirements to produce one unit of X and Y are as follows: $\begin{array}{cc}&\text { Product A } & \text { Product B } \\\text { Labour hours per unit }&1&2 \\\text { Machine hours per unit }&5&1\end{array}$

-Refer to Figure 25-3. What is the constraint on labour hours for Tiffany Manufacturing Company?

A)10X + 90Y $\le$ 200
B)1X + 2Y $\le$ 400
C)1X + 2Y $\le$ 200
D)1X + 4Y $\le$ 400

Question 20

Figure 25-1
Hassel Company manufactures two different products, X and Y. The company has 100 kgs of materials and 300 direct labour hours available for production.
The time requirements and contribution margins per unit are as follows: $\begin{array}{lrr}&\text { Product X }&\text { Product Y }\\\text { Contribution margin per unit } & £ 4 & £ 5 \\\text { Materials per unit (lbs.) } & 1 & 2 \\\text { Direct labour hours per unit } & 4 & 2\end{array}$

-Refer to Figure 25-1. What is the equation for the constraint on materials?

A)£1X + £2Y $\le$ 100
B)£4X + £2Y $\le$ 100
C)£4X + £5Y $\le$ 100
D)£4X + £5Y $\le$ 300

Question 21

Smith Products Ltd.produces two products. The manufacture of these products is partially automated. Total available labour hours are 400, and the total available machine hours are 600. Time requirements and contribution margins per unit for each product are as follows: $\begin{array}{lrr}&\text { Product X } & \text { Product Y } \\\text { Labour hours } & 2 & 3 \\\text { Machine hours } & 4 & 2 \\\text { Contribution margin per unit } & E 5 & £ 4\end{array}$
a.What is the equation to be maximized?
b.What are the equations that express the constraints?
c.What is the greatest number of units of A that can be produced given the constraints?
d.What is the optimal solution?

Question 22

Coffee Ltd.manufactures two different miniature models of furniture, a table and a chair. The company has 500 metres of lumber, 400 machine hours, and 600 direct labour hours available for production. The miniature tables and chairs provide £5 and £4 of contribution margin, respectively.
The time and lumber requirements to build a miniature table or chair are as follows: $\begin{array}{lll}&\text { Table } & \text { Chair } \\\text { Metres oflumber per unit } & 5 & 2 \\\text { Machine hours per unit } & 2 & 3 \\\text { Direct labour hours per unit } & 4 & 2\end{array}$
a.What is the objective function being maximized?
b.What are the constraint equations?
c.Graph the constraint equations. Identify the feasible region.
d.What is the optimal solution?

Question 23

Figure 25-7
The following information is available for the Johnson Boat Company, which sells two products: $\begin{array}{lcc}&\text { 3- Person Raft } & \text { Kayak } \\&\text { (Variable } A \text { ) } & \text { (Variable B) }\\\text { Selling price } & £ 50 & £ 80 \\\text { Variable costs } & £ 35 & £ 50 \\\text { Fixed costs (average) } & £ 10 & £ 20 \\\text { Processing time } & 2 \text { hours } & 4 \text { hours } \\\text { Vinyl cover used } & 16 \mathrm{sq} . \mathrm{ft} . & 12 \mathrm{sq} . \mathrm{ft} .\end{array}$
There are 100 hours available in the plant and 75 square metres of vinyl available per operating period.

-Refer to Figure 25-7. The objective function for this production situation is to:

A)maximize £15A + £30B.
B)maximize £50A + £80B.
C)maximize £35A + £50B.
D)minimize £15A + £30B.

Question 24

Figure 25-7
The following information is available for the Johnson Boat Company, which sells two products: $\begin{array}{lcc}&\text { 3- Person Raft } & \text { Kayak } \\&\text { (Variable } A \text { ) } & \text { (Variable B) }\\\text { Selling price } & £ 50 & £ 80 \\\text { Variable costs } & £ 35 & £ 50 \\\text { Fixed costs (average) } & £ 10 & £ 20 \\\text { Processing time } & 2 \text { hours } & 4 \text { hours } \\\text { Vinyl cover used } & 16 \mathrm{sq} . \mathrm{ft} . & 12 \mathrm{sq} . \mathrm{ft} .\end{array}$
There are 100 hours available in the plant and 75 square metres of vinyl available per operating period.

-Refer to Figure 25-7. The constraint equation representing the materials available for the production processes is:

A)2A + 4B > 100.
B)16A + 12B = 75.
C)2A + 4B = 200.
D)16A + 12B < 75.

Question 25

A linear programming model would NOT include which of the following items?

A)independent variables
B)constraints
C)objective function
D)networks

Question 26

Figure 25-6
Anderson Company manufactures two different products: A and B. The company has 100 kgs of raw materials and 300 direct labour-hours available for production.
The time requirements and contribution margins per unit are as follows: $\begin{array}{lcr}&A&B\\\text { Raw materials per unit (lbs.) } & 1 & 2 \\\text { Direct-labour hours per unit } & 4 & 2 \\\text { Contribution margin per unit } & E 4 & E 5\end{array}$

-Refer to Figure 25-6. What is the equation for the constraint on direct labour?

A)£1A + £2B < 300
B)£4A + £2B < 100
C)£4A + £5B < 100
D)£4A + £2B < 300

Question 27

Figure 25-6
Anderson Company manufactures two different products: A and B. The company has 100 kgs of raw materials and 300 direct labour-hours available for production.
The time requirements and contribution margins per unit are as follows: $\begin{array}{lcr}&A&B\\\text { Raw materials per unit (lbs.) } & 1 & 2 \\\text { Direct-labour hours per unit } & 4 & 2 \\\text { Contribution margin per unit } & E 4 & E 5\end{array}$

-Refer to Figure 25-6. What is the equation for the constraint on raw materials?

A)£1A + £2B < 100
B)£4A + £2B < 100
C)£4A + £5B < 100
D)£4A + £5B < 300

Question 28

Figure 25-7
The following information is available for the Johnson Boat Company, which sells two products: $\begin{array}{lcc}&\text { 3- Person Raft } & \text { Kayak } \\&\text { (Variable } A \text { ) } & \text { (Variable B) }\\\text { Selling price } & £ 50 & £ 80 \\\text { Variable costs } & £ 35 & £ 50 \\\text { Fixed costs (average) } & £ 10 & £ 20 \\\text { Processing time } & 2 \text { hours } & 4 \text { hours } \\\text { Vinyl cover used } & 16 \mathrm{sq} . \mathrm{ft} . & 12 \mathrm{sq} . \mathrm{ft} .\end{array}$
There are 100 hours available in the plant and 75 square metres of vinyl available per operating period.

-Refer to Figure 25-7. Which of the following statements is NOT correct?

A)The materials constraint favours kayaks over rafts.
B)The time constraint favours rafts over kayaks.
C)The material constraint favours rafts over kayaks.
D)The objective function favours kayaks over rafts.

Question 29

A linear programming problem has an objective function of 10a + 12b. If the optimal solution provided by the model is to produce and sell 400 units of a and 1,000 units of b, the expected profit is:

A)£1,400.
B)£14,800.
C)£16,000.
D)£40,800.

Question 30

A linear programming problem has the following objective function:
20A + 40B + 60C
If the optimal solution provided by the model is to produce and sell 100, 200, and 300 units of A, B, and C, respectively, what is the expected profit?

A)£36,000
B)£120
C)£24,000
D)£28,000