Quantitative Methods in Business Exam 1

Given the following linear program that maximizes revenue: Max Z = 15 x + 20 y s.t. 8 x + 5 y ≤ 40 4 x + y ≥ 4

$160

A university is planning a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even?

$175

Assume that x 2, x 7 and x 8 are the dollars invested in three different common stocks from New York Stock Exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock 2". The constraint for this requirement can be written as:

.4 x 2 - .6 x 7 - .6 x 8 ≤ 0.

Administrators at a university will charge students $150 to attend a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even?

24

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?

2R + 4D ≤ 480

Company A has a fixed cost of 75,000 and a variable cost of 15. Company B's fixed cost is 90,000 and variable cost is 11. At what point is Yowzah indifferent between the two bidders?

3750

Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit?

45,000

Which of the following could not be a linear programming problem constraint?

A + B ≤ -3

Which of the following statements about infeasible problems is best?

All of the possible solutions violate at least one constraint.

Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased?

B = 150, M = 0

If fixed costs decrease, but variable cost and price remain the same, the break-even point:

Decreases

In a linear programming problem, a valid objective function can be represented as:

Max 3 x + 3 y + 1/3 z

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What are the optimal daily production quantities of each product and the optimal daily profit?

R = 90, D = 75, Z = $420

A hot dog manufacturer wishes to minimize the cost in dollars of producing a low-cost niched product while meeting the dietary guidelines for protein and sodium. Once the model has been run, the surplus variable in the sodium constraint has a value of 1300 milligrams. The best interpretation of this outcome is:

The minimum cost hot dog has 1300 milligrams more sodium than required.

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

a constraint

In the formulation of a ≥ constraint:

a surplus variable is subtracted.

In a multiperiod scheduling problem, the production constraint usually takes the form of:

beginning inventory - demand + production = ending inventory.

The indicator that results in total revenues being equal to total cost is called the:

break-even point.

If the price increases, but fixed and variable costs do not change, the break-even point:

decreases

A model is a functional relationship that includes:

equations. variables. parameters.

The region that satisfies all of the constraints in a graphical linear programming problem is called the:

feasible solution space

________ are generally independent of the volume of units produced and sold.

fixed costs

When systematically formulating a linear program, the first step is to:

identify the decision variables.

For a maximization problem, the shadow price measures the ________ in the value of the optimal solution, per unit increase for a given ________.

improvement, resource

A slack variable:

is the amount by which the left side of a ≤ constraint is smaller than the right side

The optimal solution to a linear programming model that has been solved using the graphical approach:

is typically at some corner of the feasible region.

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. For the production combination of 135 cases of regular and 0 cases of diet soft drink, which resources will not be completely used?

only time

Sensitivity analysis is the analysis of the effect of ________ changes on the ________.

parameter, optimal solution

The purpose of break-even analysis is to determine the number of units of a product to sell that will:

result in 0 profit

For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs. and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the:

same product mix, different total profit.

Variable cost does not include:

staff and management salaries.

A shadow price reflects which of the following in a maximization problem?

the marginal gain in the objective that would be realized by adding one unit of a resource

At the break-even point:

total revenue equals total cost.

Use the constraints given below and determine which of the following points is feasible. (1) 14 x + 6 y ≤ 42 (2) x - y ≤ 3

x = 1; y = 4

What combination of x and y is a feasible solution that minimizes the value of the objective function? Min Z = 3x + 15y (1) 2x + 4y ≥ 12 (2) 5x + 2y ≥10

x = 6; y = 0

For a resource constraint, either its slack value must be ________ or its shadow price must be ________.

zero, zero