A revolutionary nutritionist is devising a new diet based on only 3 basic foods. The amount...
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A revolutionary nutritionist is devising a new diet based on only 3 basic foods. The amount of protein, sugar, and vitamins provided by each food and the cost per serving is displayed below. Food Cost per serving Chocolate bar 2 Cookies Ice cream Protein (g) Sugar (g) Vitamins (g) 2 1 2 1 1 3 4 3 1 2 6 The daily requirement for protein, sugar, and vitamins is 100g, 50g, and 25g. A balanced diet should satisfy: The daily requirement for protein, sugar, and vitamins. The number of servings of chocolate bars should be at least twice the number of servings of cookies and ice cream combined The amount of money spent on ice cream should be less than or equal to the amount of money spent on cookies The goal of the nutritionist is to create a minimal-cost diet. 1. Formulate the problem as a linear program by following these steps: a. Precisely define decision variables for the model b. State the objective function c. State the constraint(s) that ensure that the diet satisfies the daily requirement for protein, sugar, and vitamins d. State the constraint(s) that ensure that the number of servings of chocolate bars should be at least twice the number of servings of cookies and ice cream combined e. (5) State the constraint(s) that ensure that the amount of money spent on ice cream should be less than or equal to the amount of money spent on cookies Consider that now the goal is to balance the amount of servings (ignoring the cost) of chocolate bars, cookies, and ice cream in the diet. Note that it is impossible to achieve perfect balance (i.e., servings of chocolate bars = servings of cookies = serving of ice cream) because of the problem constraints. However, consider for example two solutions: Solution 1: 1000 chocolate bars, 10 cookies, O ice cream Solution 2: 500 chocolate bars, 200 cookies, 20 ice cream Your objective should prefer solution 2 over solution 1 as it is more "balanced". There are several different ways to achieve balance as defined above. 2. Formulate a new model to achieve this new goal (please only define the new objective, variables, and/or constraints needed and assume that the new model already includes all the constraints defined in the previous question). Consider the following situation. There is a shortage of chocolate bars so they are now priced at 2 dollars per serving for the first 50 servings and priced at 5 dollars per serving for any additional serving that a buyer gets. (Example: if you get 10 servings the cost is 20=2x10 dollars, if you get 60 servings the cost is 150=2x50+5x10 dollars). 3. Formulate a new model to create a minimal-cost diet that accounts for the special pricing described above (please only define the new objective, variables, and/or constraints needed and assume that the new model already includes all the constraints defined in part 1). A revolutionary nutritionist is devising a new diet based on only 3 basic foods. The amount of protein, sugar, and vitamins provided by each food and the cost per serving is displayed below. Food Cost per serving Chocolate bar 2 Cookies Ice cream Protein (g) Sugar (g) Vitamins (g) 2 1 2 1 1 3 4 3 1 2 6 The daily requirement for protein, sugar, and vitamins is 100g, 50g, and 25g. A balanced diet should satisfy: The daily requirement for protein, sugar, and vitamins. The number of servings of chocolate bars should be at least twice the number of servings of cookies and ice cream combined The amount of money spent on ice cream should be less than or equal to the amount of money spent on cookies The goal of the nutritionist is to create a minimal-cost diet. 1. Formulate the problem as a linear program by following these steps: a. Precisely define decision variables for the model b. State the objective function c. State the constraint(s) that ensure that the diet satisfies the daily requirement for protein, sugar, and vitamins d. State the constraint(s) that ensure that the number of servings of chocolate bars should be at least twice the number of servings of cookies and ice cream combined e. (5) State the constraint(s) that ensure that the amount of money spent on ice cream should be less than or equal to the amount of money spent on cookies Consider that now the goal is to balance the amount of servings (ignoring the cost) of chocolate bars, cookies, and ice cream in the diet. Note that it is impossible to achieve perfect balance (i.e., servings of chocolate bars = servings of cookies = serving of ice cream) because of the problem constraints. However, consider for example two solutions: Solution 1: 1000 chocolate bars, 10 cookies, O ice cream Solution 2: 500 chocolate bars, 200 cookies, 20 ice cream Your objective should prefer solution 2 over solution 1 as it is more "balanced". There are several different ways to achieve balance as defined above. 2. Formulate a new model to achieve this new goal (please only define the new objective, variables, and/or constraints needed and assume that the new model already includes all the constraints defined in the previous question). Consider the following situation. There is a shortage of chocolate bars so they are now priced at 2 dollars per serving for the first 50 servings and priced at 5 dollars per serving for any additional serving that a buyer gets. (Example: if you get 10 servings the cost is 20=2x10 dollars, if you get 60 servings the cost is 150=2x50+5x10 dollars). 3. Formulate a new model to create a minimal-cost diet that accounts for the special pricing described above (please only define the new objective, variables, and/or constraints needed and assume that the new model already includes all the constraints defined in part 1).
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Operations Management Managing Global Supply Chains
ISBN: 978-1506302935
1st edition
Authors: Ray R. Venkataraman, Jeffrey K. Pinto
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