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# Linear Programming to Determine Largest Profit Possible

1. The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: Carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good-quality redwood. Each bench that Outdoor Furniture makes requires 4 labor hours and 10 feet of redwood; each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will result in a profit of \$9 each, and picnic tables will result in a profit of \$20 each. How many tables and benches should Outdoor Furniture produce to obtain the largest possible profit?

2. The National Credit Union has \$250,000 available to invest in a 12-month commitment. The money can be placed in Treasury notes yielding an 8% return or in municipal bonds at an average rate of return of 9%. Credit union regulations require diversification to the extent that at least 50% of the investment be placed in Treasury notes. Because of defaults in such municipalities as Cleveland and New York, it is decided that no more than 40% of the investment be placed in bonds. How much should the National Credit Union invest in each security so as to maximize its return on investment? (10 points)
a. Use Excel to determine an optimal solution.
b. Request an Answer and Sensitivity Analysis.
i. Is there any slack in the optimal solution?
ii. Are there binding or non-binding constraints? Is so, name them.
iii. Are there any changes that could be made to maximize investments according to the Sensitivity Report?

#### Solution Summary

The solution uses linear programming to determine the largest profit possible for two different companies.

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