Linear programming 1. Dwight is an elementary school teacher who also raises pigs for supplemental income. He is trying to decide what to feed his pigs. He is considering using a combination of pig feeds available from local suppliers. He would like to feed the pigs at minimum cost while also making sure each pig receives an adequate supply of calories and vitamins. The cost , calorie content, and vitamin content of each feed is given in the table below. Contents Feed Type A Feed Type B Calories ( per pound) 800 1000 Vitamins (per pound) 140 units 70 units Cost ( per pound) $ 0.40 $ 0.80 Each pig requires at least 8,000 calories per day and at least 700 units of vitamins. A further constraint is that no more than 1/3 of the diet ( by weight ) can consist of Feed Type A, since It contains an ingredient that is toxic if consumed in too large a quantity. Formulate and solve a linear programming model for this problem on a spreadsheet. 2. Ed Butler is the production manager for the Bilco Corporation, which produces three types of spare parts for automobiles . The manufacture of each part requires processing on each of two machines , with the following processing times ( in hours) Spare Part Machine A B C 1 0.02 0.03 0.05 0.05 0.02 0.04 Each machine is available 40 hours per month. Each part manufactured will yield a unit profit as follows: Spare Part A B C Profit $50 $ 40 $30 Formulate and solve a linear programming model for this problem on a spreadsheet.A B C D E F Feed Type A Feed Type B Cost Daily Requirements Feed Type A Feed Type B Calories (per pound) 800 1000 7999.6 >= 8000 Vitamins (per pound) 140 70 799.96 >= 700 Cost (per pound) 0.40 $ 0.80 5.714