Section 1

Financial - Investment Decision

PyraMax Bank has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans.

The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.

Part 1

What is the amount of funds that Pyramax Bank should allocate to each type of loan in order to maximize the total annual return for the new funds?

Let: H = be the amount allocated to home loans
P = be the amount allocated to personal loans
A = be the amount allocated to automobile loans

Question #1

Write the decision variables.

Question #2

Write the objective function using the decision variables (what does Pyramax Bank want to maximize or minimize in this problem)?

Question #3

Write the constraints (limitations) using the decision variables.

Question #4

Combine the objective function and constraints to write a complete LP model for Pyramax Bank to solve their problem.

Part 2

Solve the problem using Microsoft Excel. Be sure to generate the Sensitivity Analysis report with the solution.

Question #1

Identify the optimal solution for Pyramax Bank - how much should be allocated to each type of loan.

Question #2

Identify the total annual return for Pyramax Bank.

Section 2

SENSITIVITY ANALYSIS

Question #1
If the interest rate on home loans increased to 9%, would the amount allocated to each type of loan change? Explain.

Question #2
Suppose the total amount of new funds available was increased by $100,000. What effect would this have on the total annual return? Explain.

Section 3

Operations Management - Make-or-Buy Decision

Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec's production schedule calls for at least 5000 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are as follows:

Component Manufacturing Cost Purchase Cost
Frame $38.00 $51.00
Support $11.50 $15.00
Strap $6.50 $7.50

Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department is as follows:

Component Cutting Milling Shaping
Frame 3.5 2.2 3.1
Support 1.3 1.7 2.6
Strap 0.8 --- 1.7

The available capacity (in hours) for the three departments is as follows:

Capacity (hours) 350 420 680

How many of each component should be manufactured and how many should be purchased?

Let FM = number of frames manufactured
FP = number of frames purchased
SM = number of supports manufactured
SP = number of supports purchased
TM = number of straps manufactured
TP = number of straps purchased

Question #1
Write the decision variables.

Question #2
Write the objective function using the decision variables (what does Frandec Company want to maximize or minimize in this problem)?

Question #3
Write the constraints (limitations) using the decision variables. (Hint: For the production constraint of at least 5,000 Liftmasters, it needs to be represented in three separate constraints - one for the frames, supports, and straps. Think about how many of each component is required to make one Liftmaster product. This will help to define the production constraints then for each component.)

Question #4
Combine the objective function and constraints to write a complete LP model for The Frandec Company to solve their problem.

Part 2

Question #1
Identify the optimal solution for the Frandec Company - how many frames, supports and straps should be manufactured and/or should be purchased to minimize total cost?

Question #2
Identify the total minimum cost of the manufacturing and purchasing plan.

Section 2

SENSITIVITY ANALYSIS

Question #1
How much should Frandec be willing to pay for an additional hour of time in the shaping department?

Question #2
Another manufacturer has offered to sell frames to Frandec for $45 each. Could Frandec improve its position by pursuing this opportunity? Why or why not?