Question # 2. (3 Marks) Mr. Amer raises goats for market. He wishes to determine the quantities of the available types of feed (corn, tankage, and alfalfa) that should be given to each goat. Since goats will eat any mix of these feed types, the objective is to determine which mix will meet certain nutritional requirements at a minimum cost. The number of units of each type of basic nutritional ingredient contained within a kilogram of each feed type is given in the following table, along with the daily nutritional requirements and feed costs: Nutritional ingredient kg of Corn Kg of Tankage Kg of Alfalfa Minimum daily requiremen t 200 180 150 Carbohydrates Protein Vitamins Cost (SAR) 90 30 10 84 20 80 20 72 40 60 60 60 A decision now needs to be made about determining which mix will meet certain nutritional requirements. a. (1 Mark) Formulate a linear programming model for this problem. b. [1 Mark] Solve the problem and discuss the optimal solution obtained upon solving (show the output of the software you used). c. (0.5 Mark] What is the optimal solution to the problem? d. [0.5 Mark] What is the optimal objective value? ANSWER Solution: a. Linear Programming Model Let x = quantities of corn feed x = quantities of tankage feed x = quantities of alfafa feed Minimize Z = 84x, +72x,+ 60x, Subject to constraints: 90x+ 20x, + 40x, 7200 30x, + 80x, + 60x,7180 10x + 20x,+ 60x,7150 X, X, x, mo BUS 242 Assignment 1 Semester 422 5