__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.

**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.

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__Using Microsoft Excel Solver__

**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.

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__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**.

__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.

__Using Microsoft Excel Solver__

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

__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.

__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?

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