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## Analytics for Managerial Decision-Making

Part I

1. (10 points) Chapter 1 Problem 8. Skip part (c). For part (d), you may consider using the Linear Programming module of POM-QM.
Recall the production model from Section 1.3:

Suppose the firm in this example considers a second product that has a unit profit of \$5 and requires 2 hours of production time for each unit produced. Use y as the number of units of product 2 produced.
a. Show the mathematical model when both products are considered simultaneously.
b. Identify the controllable and uncontrollable inputs for this model.
c. Draw the flowchart of the input–output process for this model (see Figure 1.5).
d. What are the optimal solution values of x and y?
e. Is the model developed in part (a) a deterministic or a stochastic model? Explain.

2. (15 points) Ponderosa Development Corporation (PDC) is a small real estate developer that builds only one style house.

• The selling price of the house is \$115,000.
• Land for each house costs \$55,000 and lumber, supplies, and other materials run another \$28,000 per house.
• Total labor costs are approximately \$20,000 per house.
• Ponderosa leases office space for \$2,000 per month. The cost of supplies, utilities, and leased equipment runs another \$3,000 per month.
• The one salesperson of PDC is paid a commission of \$2,000 on the sale of each house. PDC has seven permanent office employees whose monthly salaries are given in the table below:
Employee Monthly Salary
President \$10,000
VP, Development 6,000
VP, Marketing 4,500
Project Manager 5,500
Controller 4,000
Office Manager 3,000
Receptionist 2,000

a) Identify all costs and denote the marginal cost and marginal revenue for each house.
b) Write the monthly cost function c (x), revenue function r (x), and profit function p (x).
c) What is the breakeven point for monthly sales of the houses?
d) What is the monthly profit if 12 houses per month are built and sold?
e) Determine the BEP for monthly sale of houses graphically.

3. (15 points) Chapter 1 Problem 10
A retail store in Des Moines, Iowa, receives shipments of a particular product from Kansas City and Minneapolis. Let
X=5 number of units of the product received from Kansas City
Y= 5 number of units of the product received from Minneapolis
a. Write an expression for the total number of units of the product received by the retail store in Des Moines.