Question

1. An investor has the available profitable investment activities A and B. Investment on activity A can get a 2% annual interest rate. Investment on activity B can get a 4% annual interest rate. Also, investing activities C and D are also available. Investment on activity C can get a 5% annual interest rate. Investment on activity D can get a 7% annual interest rate. The total amount invested for activities A and B must be at least as great as the total amount invested for activities C and D. At least 25% of total investment, but no more than 40% of total investment should be made for activity C. Investment on activity D should no more than the total investment on activities A and C.

The investor starts with $50,000 and wants to know the way, which will maximize the amount of money he will receive at the end of the year. Formulate a linear programming model for this problem. (**No need to solve using Excel)

Answer 1

Le the amount investment in each activities be denoted by their letter then we can formulate this as

Maximize 0.02A + 0.04B + 0.05C + 0.07D

Subject to

A + B > = C + D

C >= 0.25A + 0.25B + 0.25C + 0.25D

C <= 0.4A + 0.4B + 0.4C + 0.4D

D <= A + C

A + B + C + D < = 50000

A, B, C, D >= 0

We can further standardize this as

Maximize 0.02A + 0.04B + 0.05C + 0.07D

Subject to

A + B – C – D >= 0

0.25A + 0.25B – 0.75C + 0.25D <= 0

A + C – D >= 0

A + B + C + D <= 50000

A, B, C, D >= 0