# Linear Programming Help (Management Science)

## EC Problem Listing

 All of the problems described below are taken from the 4th edition of a McGraw-Hill text entitled “Operations Management,” authored by Stevenson and Ozgur. This was the text formerly used for instruction in BMDS3371 until it went out of print in early 2013. EC Problem #1 Aviation Electronics produces three types of switching devices. Each type involves a two-step assembly operation. The assembly times are shown in the table below. Assembly Time per Unit Station #1 Station #2 Model A 2.5 minutes 3.0 minutes Model B 1.8 minutes 1.6 minutes Model C 2.0 minutes 2.2 minutes Each workstation has a daily working time of 7.5 hours. Manager Bob Parkes wants to obtain the greatest possible profit during the next five working days. Model A yields a profit of \$8.25 per unit, Model B a profit of \$7.50 per unit, and Model C a profit of \$7.80 per unit. Assume the firm can sell all it produces during this time but it must fill outstanding orders for 20 units of each model type. Formulate the linear programming model of this problem. Solve the model to show the maximum amount of profit possible given the constraints outlined above. EC Problem #2 A farm consists of 600 acres of land, of which 500 acres will be planted with corn, soybeans, and wheat, according to these conditions: a.) At least half of the planted acreage should be in corn. b.) No more than 200 acres should be soybeans. c.) The ratio of corn to wheat planted should be 2:1. It costs \$20 an acre to plant corn, \$15 an acre to plant soybeans, and \$12 an acre to plant wheat. Formulate this problem as an LP model that will minimize planting cost while achieving the specified conditions. EC Problem #3 Reproduce the LP model needed for #2 above but modify it to reflect the need to plant at least 500 acres. EC Problem #4 A high school dietician is planning menus for the upcoming month. A new item will be spaghetti with sauce. The dietician wants each serving to contain at least 10 grams of protein and at least 40 grams of carbohydrates. Spaghetti contains 5 grams of protein and 32 grams of carbohydrates per cup, and the sauce contains 4 grams of protein and 5 grams of carbohydrates per cup. For aesthetic reasons, the dietician wants the ratio of spaghetti to sauce to be 4:1. Spaghetti costs \$0.30 per cup to buy and prepare, the sauce costs \$0.40 per cup to buy and prepare. The dietician wants to minimize the cost per serving and keep the calories per serving to 330 or less. The sauce contains 100 calories per cup, and the spaghetti contains 160 calories per cup. Formulate a linear programming model that will minimize the cost per serving subject to the various constraints decribed above.