# IE 312 Midterm I October 3, 2012 Name: __________________________

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```Name: __________________________
IE 312 Midterm I
October 3, 2012
This exam is closed book and closed notes. It will last for 50 minutes. Good luck!
1. You are operating a large 10,000 acre farm where you grow vegetables or cotton and you want to develop a
planting plan that maximizes profit. Each acre of vegetables you plant returns a profit of \$450, and each acre of
cotton returns a profit of \$200. As a precaution you will plant no more than 70% in a single crop. Also, water for
irrigation is limited. Growing vegetable requires 10 units of water per acre, and cotton requires 7 units per acre.
You have a total of 70,000 units of water available for the season.
a. (15%) Formulate a linear program to find the optimal planting plan.
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b. (25%) Find the optimal solution graphically.
c. (10%) Now assume that you are required by federal regulations to plant all of your acres. Show
graphically (on the same graph) what happens and what is the new optimal solution.
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2. (50%) Your company’s new Chocolate-Chip Cookies and Chocolate-Hazelnut Cookies are so popular that your
supplier of chocolate chips and hazelnuts cannot keep up with demand. Producing each case of Chocolate Chip
Cookies requires 2 pounds of chocolate chips, and producing each case of Chocolate-Hazelnut Cookies requires 1
pound of chocolate chip cookies and 1 pound of hazelnuts. Your supplier has 2000 pounds of chocolate chips
and 400 pounds of hazelnuts available per month. Other ingredients are basic and plentiful.
Your sales territory is divided into four regions, and the demand for each type of cookie is distributed among the
four sales regions as shown below.
Chocolate-Chip
Chocolate-Hazelnut
Region 1
420
200
Region 2
340
150
Region 3
310
210
Region 4
280
100
In an effort to at least partially keep up with demand in all of the sales regions, you want to satisfy at least 50%
of the total demand in each region, and no more than 80% of the demand for each type of cookie in any region.
The sale price and logistics costs vary from region to region, but are the same for both types of cookies. The
profits obtained per case of cookies in each region are shown below.
Profit
Region 1
\$1.60
Region 2
\$1.40
Region 3
\$1.90
Region 4
\$1.20
Formulate a linear program to obtain a production and sales plan that maximizes profit.
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Extra Page
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