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QUESTION 2 a) Dr. Khadijah was assigned to oversee the diet of her patients. She has to make sure the basic nutritional requirements are satisfied, but at the same time avoid spending more than necessary. Dr. Khadijah suggests two types of 1,200-Calorie meal plan. Meal plan A costs RM35 and meal plan B costs RM30 per day. Meal A yields 26 grams of fiber, 157 grams of carbohydrate, and 68 grams of protein. Meal B yields 20 grams of fiber, 170 grams of carbohydrate, and 55 grams of protein. The minimum requirements of each nutrient are 17, 100, and 50 grams, respectively. Prior to the meal handling, total weight of the meal serving must not less than 500 grams. i. Formulate a linear programming model with the objective of minimizing total meal cost. (3 marks) ii. Hence, obtain the dual of the above model. (3 marks) b) An engineering company produces three products A, B and C using three machines M1, M2 and M3. The profits earned by the products A, B and Care RM2, RM5 and RM8 per unit respectively. A simplex optimal solution to maximize the profit is given below where X1, X2 and X3 are quantities of products A, B and C produced by the company. S1, S2 and Sg represent the slack in the resources M1, M2 and M3. The following is the simplex tableau for the problem. Basic X1 X2 X3 S1 S2 S3 RHS X2 1/3 1 0 1/6 - 1/3 0 8/3 X3 5/6 0 1 - 1/12 2/3 0 56/3 S3 7/3 0 0 - 1/13 - 1/3 1 44/3 Z 25/3 5 8 1/6 11/3 0 Cj-2 -19/3 0 0 - 1/6 - 11/3 0 i. Find the maximum profit for the above model. (2 marks) ii. State the optimal solution for the above problem. (2 marks) iii. Explain whether the optimal solution unique or not. (1 mark) iv. Which resource(s) is/are not fully utilized? State the value. (2 marks) If the company wishes to raise production, which of the three resources should be given priority for enhancement? State your reason. (2 marks) V