Optimization Exercises

Formulate the following and Solve in Excel.

A bank is trying to determine how to invest some assets. At present $500,000 is available for investment in bonds, home loans, auto loans and personal loans. The annual rate of return on each type is known to be as follows: bonds, 7%; home loans, 8%; auto loans, 13%; and personal loans, 20%. To ensure that the portfolio is not too risky, the following conditions have to be met:

The amount invested in personal loans cannot exceed the amount invested in bonds.
Home loan amount cannot exceed auto loan amount.
No more than 25% may be invested in personal loans.

Set up as a linear programming problem to maximize the bank’s return on the investment portfolio.

You want to mix two types of food to feed your horses at the lowest cost, yet provide some minimum nutrients. One packet of Food A contains 5 mg of nutrient 1 and 10 milligrams of nutrient 2. One packet of Food B contains 7 mg of nutrient 1 and 3 milligrams of nutrient 2. The horses need at least 50 mg of nutrient 1 and 40 milligrams of nutrient 2 per day. Each packet of Food A costs $5.00, while Food B costs $ 3.00. How many packets of each food type would you mix together to minimize the cost?

Volunteers work for your non-profit for 2 weeks at a stretch in the summer. The total time span is 6 weeks where you need volunteers. You need 10 in week 1, 7 in week 2, 8 in week 3, 12 in week 4, 7 in week 5 and 7 in week 6. Those who begin work in any of the first 5 weeks continue to work for 2 weeks from the time they begin. However, those you begin in week 6 only work for that week, and then your summer project is done. How would you minimize the number of volunteers needed to satisfy the requirements?

Transportation costs per unit from sources to destinations are as follows, and the corresponding demands and supplies are given. Set up as an LP problem.

Factory A