Question
The Finesse company is going to introduce a packaged trial mix as a new product with the code name ZADI - 5. The ingredients for
The Finesse company is going to introduce a packaged trial mix as a new product with the code name ZADI - 5. The ingredients for the trial mix are Sunflower Seeds, Thompson Raisins, Oat Flakes, Pecans, and Dried Apples. Each ingredient contains certain amounts of Vitamins, Minerals, Protein, and Calories per pound. The Nutrition Research department has specified that the product be designed so that a certain nutritional profile (in terms of amount per pound) is met:
- The amount of Vitamins should be minimum 10 g.
- The amount of Minerals should be no less than 10 g.
- The amount of Proteinshould be at least 15 g.
- The number of Calories should be equal to or greater than 600 .
The specialists of Marketing department including Humber graduates Krystyna, Trang, Nancy should determine the optimal product composition that will minimize the product cost per pound. The data shown below (and the link to the Excel file) summarize the parameters of the problem. Every component line shows the quantities per pound. Note that NR means Nutritional Requirement.
Components Sunflower Thompson Oat Dried Pecans NR Seeds Raisins Flakes Apples Vitamins 1.55 4.05 4.98 3.86 5 10 Minerals 3.75 5.03 2.97 7.87 2.05 10 Protein 2.08 3.78 7.92 8.04 5 15 Calories 493 447 158 296 491 600 Cost($/pound) 3.25 4.15 4.05 6.05 4.1 Download CSV (a) The model requires the following decision variables: O1 = Vitamins, 22 = Minerals, 23 = Protein, 24 = Calories Or; = cost of ingredient i per pound Or1 = Sunflower Seeds, 2 = Thompson Raisins, 23 = Oat Flakes, 24 = Pecans, $5 = Dried Apples Orij = gramms of component i in ingredient j O None of the above.OZ = 3.25x1 + 4.15x222 + 4.05x22 + 6.05233 + 4.1x44 OZ = 10rj1 + 1022 + 15233 + 600:44 O Z = 3.25x1 + 4.15x2 + 4.05x3 + 6.05x4 + 4.1x5 OZ = 10x1 + 10x2 + 1523 + 600x4 ONone of the above.(c) Please choose the correct Vitamins constraint: Ol + 22 + 23 + 24 + 25 10 O1.55x1 + 3.75x2 + 2.08x3 + 493x4 10 Oeach x2j > 10 Oxi + 22 + 3 + 4 + 5 15 Oml + 2 + 3 + 4 + as 15 O None of the above.(f) Please choose the correct Calories constraint: O 4931 + 447x2 + 158x3 + 29624 + 491x5 > 600 0 3.86x1 + 7.87x2 + 8.04x3 + 29624 - 600 Ol + 2 + 23 + 4 + 5 600 O None of the above. (g) Select the correct non-negativity constraint for this LP problem. Oxi X x2 X 23 X C4 X 25 2 0 Oml + 2 + 3 + 24 20 Oall c; > 0, i = 1, 2, 3, 4, 5 O at least one rij 2 0 O None of the above.To determine the optimal product composition that minimizes the product cost Humber graduates Krystyna, Trang, Nancy applied the Excel Solver to this LP model. Do the same and answer the following questions. Please round all values to 2 decimal places. In the Sensitivity Report part, please use rounded Allowable Increase/Decrease value in the intermediate calculations. (h) The optimal amounts (in g) are Sunflower Seeds = Thompson Raisins = Oat Flakes = Pecans = Dried Apples = with the Total Cost of $ (i) Does the Excel Answer Report show any binding constraint? O One constraint is not binding. O Two constraints are not binding. O Yes, all constraints are binding. O No, there are no binding constraints. O None of the above.(i) It is known that Excel Sensitivity Report provides analysis of how changes in the coefficients of an LP problem affect the optimal solution. In this case, it shows that, for example, If the cost of the Sunflower Seeds increases by $ to $ or drops by $ to $ then the optimal solution will not change. If the cost of the Sunflower Seeds goes beyond these limits, then the optimal solution will move to another corner pointStep by Step Solution
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