Needed only d and e
1. (26 points) Patterson Nut Company wishes to introduce packaged trail mix as a new product. The five ingredients for the trail mix are: seeds, raisins, granola, pecans and walnuts. Each ingredient contains a certain amount of vitamins, minerals, protein, and calories. The market- ing department has specified the product be designed so that a certain minimum nutritional profile is met. The data shown below summarize the parameters of the problem. Vitamins Minerals Protein Calories Cost/pound Units per Pound Nutritional Seeds Raisins Granola Pecans Walnuts Requirement 10 20 10 30 20 16 5 7 4 9 2 10 1 4 10 2. 1 15 500 450 160 300 500 600 $4 $5 $3 $7 S6 This data can be interpreted as follows. The trail mix should have at least 16 units of vitamins, at least 10 units of minerals, at least 15 units of protein, and at least 600 calories. The columns associated with each ingredient provide us their nutritional composition and cost. For example, a pound of seeds provides 10 units of vitamins, 5 units of minerals, 1 unit of protein, 500 calories, and costs $4. Patterson would like to determine the product composition of a trail mix that meets these nutritional requirements at minimum cost. (a) Write a mathematical linear program for the above optimization problem, including clearly defined decision variables, objective function, and constraints. (b) Implement and solve your linear programming model in Solver. Your Excel file submis- sion should contain your Solver Model for this part. (c) What is the optimal product composition? That is, how much of each of the five ingre- dients should be in the trail mix? State in words. (d) What is the cost of this optimal product composition? State in words. (e) Patterson's owner insists that each of the trail mix ingredients makes up at least 15% of the overall trail mix. i) Indicate mathematically how to modify your model to incorpo- rate this requirement, and ii) Implement your modification (do this in a separate sheet containing its own Solver Model) to determine the new optimal product composition and cost. State the new optimal product composition and its cost. (To obtain full credit the modified model should be linear). Your Excel file submission should contain your Solver Model for this part. 1. (26 points) Patterson Nut Company wishes to introduce packaged trail mix as a new product. The five ingredients for the trail mix are: seeds, raisins, granola, pecans and walnuts. Each ingredient contains a certain amount of vitamins, minerals, protein, and calories. The market- ing department has specified the product be designed so that a certain minimum nutritional profile is met. The data shown below summarize the parameters of the problem. Vitamins Minerals Protein Calories Cost/pound Units per Pound Nutritional Seeds Raisins Granola Pecans Walnuts Requirement 10 20 10 30 20 16 5 7 4 9 2 10 1 4 10 2. 1 15 500 450 160 300 500 600 $4 $5 $3 $7 S6 This data can be interpreted as follows. The trail mix should have at least 16 units of vitamins, at least 10 units of minerals, at least 15 units of protein, and at least 600 calories. The columns associated with each ingredient provide us their nutritional composition and cost. For example, a pound of seeds provides 10 units of vitamins, 5 units of minerals, 1 unit of protein, 500 calories, and costs $4. Patterson would like to determine the product composition of a trail mix that meets these nutritional requirements at minimum cost. (a) Write a mathematical linear program for the above optimization problem, including clearly defined decision variables, objective function, and constraints. (b) Implement and solve your linear programming model in Solver. Your Excel file submis- sion should contain your Solver Model for this part. (c) What is the optimal product composition? That is, how much of each of the five ingre- dients should be in the trail mix? State in words. (d) What is the cost of this optimal product composition? State in words. (e) Patterson's owner insists that each of the trail mix ingredients makes up at least 15% of the overall trail mix. i) Indicate mathematically how to modify your model to incorpo- rate this requirement, and ii) Implement your modification (do this in a separate sheet containing its own Solver Model) to determine the new optimal product composition and cost. State the new optimal product composition and its cost. (To obtain full credit the modified model should be linear). Your Excel file submission should contain your Solver Model for this part
