Section A: Linear Optimization (Worth 25 marks) The Whole Food Nutrition Center uses three bulk grains, A, B, and C, to blend a natural cereal that it sells by the pound. The cost of each bulk grain is indicated in the table below, along with the units of four types of nutrient (Nutrient 1, 2, 3, and 4) that is contained in each pound of the grains. After consulting with the nutritionist, Whole Food has determined that each pound serving of the cereal should contain 24 units of Nutrient 1, 16 units of Nutrient 2, 8 units of Nutrient 3, and 3.4 units of Nutrient 4. Whole Food wishes to decide how to blend the three types of grain in order to minimize the total cost of each pound of the cereal. In other words, they wish to solve the following optimization: Minimize 33A + 47B + 38C Subject to: 22A + 28B + 21C > 24 16A + 14B + 25C 2 16 8A + 7B + 90 2 8 5A + 6C 2 3.4 A + B + C =1 A, B,C 2 0 Grain A Grain B Grain C Nutritionist's requirement Nutrient 1 22 28 21 24 Nutrient 2 16 14 25 16 Nutrient 3 8 7 9 8 Nutrient 4 5 0 6 3.4 Cost per pound of grain (cents) 33 47 38 (A1). Please help Whole Food solve the problem (e.g., in Excel using Solver) and obtain the results. Report the results to the manager of Whole Food in plain English. (5 marks) (A2). Based on your work for Question (A1), how many constraints regarding the nutrients are binding? For each of the non-binding constraints, what is the surplus? (5 marks) (A3). How sensitive is Whole Food's blending strategy to the cost per pound for each type of grains individually? Which is it most sensitive to? (5 marks) (A4). If the cost of Grain A changes to 37 cents per pound, while all other costs remain the same, should Whole Food keep its current blending strategy or change it? Why or why not? (5 marks) (A5). If the nutrient requirement for Nutrient 2 increases from 16 units to 18 units, should Whole Food keep its current blending strategy? Why or why not?