Operations Research -- Sample Homework Assignments

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56:171 Operations Research mmmmmmm 56:171mmmmmmm

Operations Research -- Sample Homework Assignments
Fall 1997 Dennis Bricker Dept. of Industrial Engineering University of Iowa mmmmmmmmmmmmmmmmmmmm mmmmmmmmmm Homework #1 mmmmmmmmm Linear Programming Model Formulation: Formulate a Linear Programming model for each problem below, and solve it using LINDO (available on the HP-UX workstations, or you may use the software packaged with the textbook.) Be sure to state precisely the definitions of your decision variables, and explain in a few words the purpose of each type of constraint. Write a few words to state what the optimal solution is (i.e., without making use of variable names). (For instructions on LINDO, see §4.7 and the appendix of chapter 4 of the text.) mmmmmmmmmmmmmmmmmmmm

1. Exercise #4, page 113 (Walnut Orchard Farms)
"Walnut Orchard has two farms that grow wheat and corn. Because of differing soil conditions, there are differences in the yields and costs of growing crops on the two farms. The yields and costs are Farm 1 Farm 2 -------------------------------------------------------------------------------------------Corn yield/acre Cost/acre of corn Wheat yield/acre Cost/acre of wheat 500 bushels $100 400 bushels $90 650 bushels $120 350 bushels $80

Each farm has 100 acres available for cultivation; 11,000 bushels of wheat and 7000 bushels of corn must be grown. Determine a planting plan that will minimize the cost of meeting these demands. mmmmmmmmmmmmmmmmmmmm

2. Investment planning
I now have $100. The following investments are available at the beginning of each of the next five years: Investment A: Every dollar invested yields $0.10 a year from now and $1.30 three years after the original investment, a total of $1.40. Investment B: Every dollar invested yields $1.35 two years later.

Sample HW

Fall '97

page 1

56:171 Operations…...

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