QAUNTITATIVE TECHNIQUES SOLUTION FOR THE CASE CUTTING CAFETERIA COSTS LPP MODEL FOR CAFETERIA COST CUTTING Objective: To reduce the purchase of potato and green beans, so as to meet the conditions of the various constraints to achieve the goal of minimizing the purchase cost. Constraint conditions: PotatoesGreen Beans Protein1. 5 g per 100 g > 1. 5%2 g per 100 g > 2% Iron0. 3 mg per 100 g > 0. 3%1. 2 mg per 100 g > 1. 2% Vitamin C12 mg per 100 g > 12%10 mg per 100 g > 10% Q 1)

Determine the amount of potatoes and green beans Maria should purchase each week for the casserole to minimize the ingredient costs while meeting nutritional, taste, and demand requirements. Before she makes her final decision, Maria plans to explore the following questions independently except where otherwise indicated. Answer: 1) The decision variables are: P: The amount of potatoes purchased per week G: The amount of beans purchased per week Such that, Objective Function: Subject to constraints: The first three constraints are nutritional constraints: constraints on protein, iron, and vitamin contents respectively.

Putting these values in LINDO: Q. 2) Maria is not very concerned about the taste of the casserole; she is only concerned about meeting nutritional requirements and cutting costs. She therefore forces Edson to change the recipe to allow for only at least a one to two ratio in the weight of potatoes to green beans. Given the new recipe, determine the amount of potatoes and green beans Maria should purchase each week. Answer: In this case, the taste constraint is changed. The new constraint is: Pounds of potatoes / Pounds of green beans >1/2 So, rebuilding the model as follows: Object function & constraints:

Putting value in LINDO: LINDO obtained as follows: Objective value: 16. 22614 Variable Value Reduced Cost P 4666. 667 0. 000000 G 5500. 000 0. 000000 Row Slack or Surplus Dual Price 1 16. 22614 -1. 000000 2 0. 000000 -0. 3303965E-01 3 0. 000000 -0. 1284875 4 60. 00000 0. 00000 5 3833. 333 0. 000000 6 166. 6667 0. 000000 Conclusion: The original base solution is to change the weight ratio of edible after the base solution into, just to meet the minimum requirement of protein with iron, can be seen from the figure. Protein 180g, 80mg iron and vitamin C1050mg constraints, plus edible and the weight ratio of 1:2 minimum weekly requirements under the 10kg limit, Maria decided to buy 4666. 667 g of potatoes with 5500 g of green beans, the required to spend at $ 16. 2614. Q. 3) Maria decides to lower the iron requirement to 65 mg since she determines that the other ingredients, such as the onions and cream of mushroom soup, also provide iron. Determine the amount of potatoes and green beans Maria should purchase each week given this new iron requirement. Answer: Model Becomes as follows: LINDO obtained as follows: Objective value: 14. 29883 Variable Value Reduced Cost P 7166. 667 0. 000000 G 3625. 000 0. 000000

Row Slack or Surplus Dual Price 1 14. 29883 -1. 000000 2 0. 000000 -0. 3303965E-01 3 0. 000000 -0. 1284875 4 172. 5000 0. 000000 5 14083. 33 0. 000000 6 791. 6667 0. 000000 Conclusion: Maria decided to buy 7166. 667 g of the potato’s green beans with 3625g, the necessary cost of $ 14. 9883. Optimal solution just to meet the minimum requirement of protein and iron, vitamin C, edible weight and weekly demand constraint does not affect the feasible solution area. Q 4) Maria learns that the wholesaler has a surplus of green beans and is therefore selling the green beans for a lower price of $0. 50 per lb. Using the same iron requirement from part (c) and the new price of green beans, determine the amount of potatoes and green beans Maria should purchase each week. Answer: The model becomes as follows: Putting value in LINDO: LINDO obtained as follows:

Objective value: 10. 22490 Variable Value Reduced Cost P 5684. 211 0. 000000 G 4736. 842 0. 000000 Row Slack or Surplus Dual Price 1 10. 22490 -1. 000000 2 0. 000000 -0. 5680501E-01 3 8. 894737 0. 000000 4 105. 895 0. 000000 5 0. 000000 -0. 5796429E-05 6 421. 0526 0. 000000 Conclusion: Maria decided to buy 5684. 211 g of potatoes with 4732. 842 g of green beans, the required cost of $ 10. 2249. And found the original context two basic solutions are to reduce costs based solution into peas. Q 5) Maria decides that she wants to purchase lima beans instead of green beans since lima beans are less expensive and provide a greater amount of protein and iron than green beans.

Maria again wields her absolute power and forces Edson to change the recipe to include lima beans instead of green beans. Maria knows she can purchase lima beans for $0. 60 per lb from the wholesaler. She also knows that lima beans contain 22. 68 g of protein per 10 ounces of lima beans, 6. 804 mg of iron per 10 ounces of lima beans, and no vitamin C. Using the new cost and nutritional content of lima beans, determine the amount of potatoes and lima beans Maria should purchase each week to minimize the ingredient costs while meeting nutritional, taste, and emand requirements. The nutritional requirements include the reduced iron requirement from part (c). Answer: Lima BeansLima Beans Protein22. 68 g per 10 ounces8 g per 100 g > 8% Iron6. 804 mg per 10 ounces>2. 4 mg per 100 g > 2. 4% Vitamin C00% Model becomes as follows: Putting values in LINDO: LINDO obtained as follows: Objective value: 9. 843062 Variable Value Reduced Cost P 8750. 000 0. 000000 G 1614. 583 0. 000000

Row Slack or Surplus Dual Price 1 9. 843062 -1. 000000 2 80. 41667 0. 000000 3 0. 000000 -0. 5506608E-01 4 0. 000000 -0. 5965492E-02 5 34062. 50 0. 000000 6 364. 5833 0. 000000 Conclusion: Maria decided to buy 8750 g of potatoes with 1614. 83 g Lima beans, needed to spend the $ 9. 843062. In such a purchase combination, you can find, just meet the minimum iron and vitamin C demand , protein, edible weight ratio and the minimum demand is more than a week, meaning to say: these three restrictions type does not affect the feasible solution area. Also it can be seen if other conditions remain unchanged, the reduction of 1 unit of iron demand, can reduce the cost of 0. 055 $; in other conditions unchanged, reducing demand for 1 unit of vitamin C can reduce cost element. Q 6)Will Edson be happy with the solution in part (e)?

Why or why not? Q 7)An All-State student task force meets during Body Awareness Week and determines that All-State University’s nutritional requirements for iron are too lax and that those for vitamin C are too stringent. The task force urges the university to adopt a policy that requires each serving of an entree to contain at least 120 mg of iron and at least 500 mg of vitamin C. Using potatoes and lima beans as the ingredients for the dish and using the new nutritional requirements, determine the amount of potatoes and lima beans Maria should purchase each week.

Answer: Model becomes as follows: Putting value in LINDO: LINDO obtained as follows: Objective value: 10. 69855 Variable Value Reduced Cost X1 5714. 286 0. 000000 X2 4285. 714 0. 000000 Row Slack or Surplus Dual Price 1 10. 69855 -1. 000000 2 248. 5714 0. 000000 3 0. 000000 -0. 097755E-01 4 185. 7143 0. 000000 5 2857. 143 0. 000000 6 0. 000000 -0. 8181246E-03 Conclusion: Maria decided to buy 5714. 286 g of potatoes with 4285. 714 g of Lima beans, needed to spend to $ 10. 69855. In such a purchase combination, you can find, just meet the minimum requirement for iron and weekly demand , protein, vitamin C and weight ratio is more than edible, meaning to say: this does not affect the three constraints feasible solution area.