Question: My diet requires that all the food I eat come from one of the four "basic food groups": brownies, chocolate ice cream, cola, and pineapple cheesecake. Each day, I must ingest at most 800 calories and at least 6gr of chocolate, 10gr of sugar, 8gr of fat. Considering the data in the following table, find the minimum-cost mix of food that satisfies all my dietary requirements. Decision Variables: X1 : number of brownies included in the diet x2 : scoops of chocolate ice cream included in the diet X3 : bottles of cola included in the diet x4 : pieces of pineapple cheesecake included in the diet LP: Minz2=50x1+20x1+30x3+80x4 s.t. 400x1+200x2+150x3+500x4800 (at most 800 calories) - constraint1 3x1+2x26 (at least 6gr of chocolate) - constraint2 2x1+2x2+4x3+4x410 (at least 10 gr of sugar) - constraint 3 2x1+4x2+x3+5x48 (at least 8 gr of fat) - constraint 4 xi0i=1,2,3,4 The answer and sensitivity reports of the optimal solution are provided below. Answer the following questions. 1. What is the optimal solution (z,x1,x2,x3, and x4) ? 2. What are the reduced costs of the four decision variables? 3. What should be the cost of cheesecake so that the optimal basis does not change? What should be the cost of brownie so that the optimal basis does not change? 4. What happens if the cost of ice-cream is 25c ? 5. What are the allowable increase and decrease values of the calories and fat constraints? What are their shadow prices? If 12gr fat is required, what would be the new optimal solution to the problem? 6. What will be the new optimal solution for each of the following cases for the daily chocolate requirement? (a) it increases to 6.5gr, (b) it decreases to 4gr, and (c) it increases to 12gr ? 7. Which of the following options is better: decreasing the sugar requirement to 8 gr or buying ice-cream (with the same ingredients) from a cheaper brand for 16c/scoop ? Answer Report Sensitivity Report