Question 1

Production has indicated that they can produce widgets at a cost of $4.00 each if they lease new equipment at a cost of $10,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project?

Accepted Answer

To avoid losing money, the total revenue must cover both the variable costs of production and the fixed cost of leasing the equipment. Option B, selling 3,000 units at $7.50 each, generates $22,500 in revenue. The cost of producing 3,000 units at $4.00 each is $12,000, and when added to the lease cost of $10,000, the total cost is $22,000. This option generates a profit of $500, thus avoiding a loss.

Question 2

The objective function for a model is a mathematical expression of the measure of performance for the problem in terms of the decision variables.

Accepted Answer

The objective function is indeed a mathematical expression that measures the performance of the problem in terms of the decision variables.

Question 3

A parameter in a model is a variable that represents a decision to be made.

Accepted Answer

A parameter in a model is a quantity that influences the output or behavior of a model but is considered constant and not a decision variable. Decision variables are what we adjust to optimize the model, whereas parameters are inputs to the model that are typically fixed or given.

Question 4

Enlightened future managers should know which of the following?

Accepted Answer

Enlightened future managers should have knowledge and understanding of all the mentioned points in order to effectively utilize management science in decision-making.

Question 5

Sensitivity analysis is used to check the effect of changes in the model.

Accepted Answer

Sensitivity analysis is performed to test the impact of changes or variations in input variables, assumptions or parameters on the output or outcomes predicted by a model.

Question 6

Investigating the potential outcomes when estimates turn out to be incorrect is known as "what-if analysis."

Accepted Answer

"What-if analysis" is indeed the investigation of potential outcomes when estimates turn out to be incorrect.

Question 7

Which of the following are components of a mathematical model for decision making?

Accepted Answer

All of the answer choices are correct components of a mathematical model for decision making. Decision variables are the unknowns we want to determine in the model, the objective function is the measure of performance to be optimized, constraints are the limitations or restrictions on the decision variables, and parameters are the fixed values in the model. All of these elements are needed to construct a robust mathematical model for decision making.

Question 8

In order to produce a new product, a firm must lease equipment at a cost of $10,000 per year. The managers feel that they can sell 5,000 units per year at a price of $7.50. What is the highest variable cost that will allow the firm to at least break even on this project?

Accepted Answer

The answer of In order to produce a new product,...

Question 9

The rapid development of the management science discipline can be credited in part to:

Accepted Answer

George Dantzig, known for developing the simplex algorithm for linear programming, and the computer revolution, which provided the computational power needed to solve complex management science problems, both significantly contributed to the rapid development of the management science discipline.

Question 10

A manager has determined that a potential new product can be sold at a price of $20.00 each. The cost to produce the product is $10.00, but the equipment necessary for production must be leased for $75,000 per year. What is the break-even point?

Accepted Answer

To find the break-even point, we need to determine how many units need to be sold to cover the costs of production, including the equipment lease.

Let's first calculate the total cost of leasing the equipment for one unit:

$75,000 / 12 months = $6,250 per month
$6,250 / 10,000 units = $0.625 per unit

Now we can calculate the total cost per unit:

$10.00 (cost of production) + $0.625 (cost of equipment lease) = $10.625

To break even, the revenue from selling each unit must cover this cost. Since each unit can be sold at a price of $20.00, the profit per unit would be:

$20.00 - $10.625 = $9.375

To cover the $75,000 equipment lease, we need to generate:

$75,000 / $9.375 = 8,000 units

Therefore, the break-even point is 7,500 units.

Question 11

Which of the following is an inequality or equation that expresses a restriction in a mathematical model?

Accepted Answer

A constraint is a condition or restriction expressed as an inequality or equation that limits the set of possible solutions in a mathematical model. Therefore, option D is the correct answer. The other options are not related to restrictions in the model.

Question 12

In order to produce a new product, a firm must lease equipment at a cost of $25,000 per year. The managers feel that they can sell 10,000 units per year at a price of $15.00. What is the highest variable cost that will allow the firm to at least break even on this project?

Accepted Answer

To break even, the total revenue must equal the total costs. The total revenue from selling 10,000 units at $15.00 each is $150,000. The fixed costs are $25,000 for leasing equipment. Therefore, the total available for covering variable costs is $150,000 - $25,000 = $125,000. Dividing this by 10,000 units gives a maximum variable cost per unit of $12.50 to break even.

Question 13

A manager has determined that a potential new product can be sold at a price of $10.00 each. The cost to produce the product is $5.00, but the equipment necessary for production must be leased for $25,000 per year. What is the break-even point?

Accepted Answer

The break-even point is calculated by dividing the fixed costs by the profit per unit. The profit per unit is the selling price minus the cost to produce, which is $10.00 - $5.00 = $5.00. The fixed cost is the equipment lease, which is $25,000. Therefore, the break-even point is $25,000 / $5.00 = 5,000 units.

Question 14

A manager has determined that a potential new product can be sold at a price of $50.00 each. The cost to produce the product is $35.00, but the equipment necessary for production must be leased for $100,000 per year. What is the break-even point?

Accepted Answer

To calculate the break-even point, we need to find out how many units must be sold to cover the lease cost plus the cost of producing each unit and still make a profit of $0.

Let X be the number of units sold.

The total cost (TC) is:

TC = lease cost + (cost to produce each unit * number of units)

TC = $100,000 + ($35.00 * X)

The total revenue (TR) is:

TR = price per unit * number of units

TR = $50.00 * X

At the break-even point, TC = TR:

$100,000 + ($35.00 * X) = $50.00 * X

Solving for X:

$100,000 = $15.00 * X

X = 6,667 units

Therefore, the break-even point is 6,667 units, which corresponds to option C.

Question 15

Managers may base their decisions on which of the following?

Accepted Answer

Managers may base their decisions on quantitative factors, their best judgment, opinions from other managers, and past experience. All of these factors play a role in informed decision making.

Question 16

"What-if analysis" is a process used to generate estimates for use in mathematical models.

Accepted Answer

"What-if analysis" is a process used to explore the potential outcomes of different scenarios in decision-making, not specifically to generate estimates for use in mathematical models.

Question 17

Which of the following is a constant in a mathematical model?

Accepted Answer

A parameter is a constant value in a mathematical model. Decision variables, objective functions, and constraints all involve variables that can change depending on the situation being modeled.

Question 18

Which of the following are steps in a typical management science study?

Accepted Answer

All of the answer choices are correct steps in a typical management science study.

Question 19

Which of the following is a mathematical expression that gives the measure of performance for the problem?

Accepted Answer

The objective function is the mathematical expression that gives the measure of performance for the problem. It is typically optimized or minimized in order to achieve the desired result. The decision variable and parameter are inputs to the problem, while the constraint is a condition that must be adhered to in the optimization process.

Question 20

Management science is based strongly on which of the following fields?

Accepted Answer

The answer of Management science is based strongly on which...

Quiz 1: Introduction