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Question 3 (30 points) Paul’s company produces the drug Roza…

Question 3 (30 points) Paul’s company produces the drug Rozac from 4 chemicals. Today, they must produce at least 3,000 lb of the drug. The three active ingredients in Rozac are A, B, and C. By weight, at most 6% of Rozac must be ingredient A, at least 3% of Rozac must be ingredient B, and at most 9% of Rozac must be ingredient C. Rozac is produced by blending the 4 chemicals. The cost per pound of each chemical and the amount of each active ingredient in 1 lb of each chemical are given below in the table: Chemical Cost ($ per lb) A B C 1 7 0.11 0.02 0.07 2 14 0.06 0.03 0.13 3 12 0.10 0.05 0.08 4 9 0.14 0.09 0.04 It is necessary that at most 500 lb of chemical 3 are used. Formulate an LP that determines the cheapest way of producing today’s batch of Rozac. (You need to write all the decision variables, objective, and constraints and explain/describe EACH of them in your answer. You do NOT need to write out the parameters in this numerical example.)

Question 3 (30 points) Paul’s company produces the drug Roza…

Question 3 (30 points) Paul’s company produces the drug Rozac from 4 chemicals. Today, they must produce at least 1,500 lb of the drug. The three active ingredients in Rozac are A, B, and C. By weight, at most 12% of Rozac must be ingredient A, at least 5% of Rozac must be ingredient B, and at least 7% of Rozac must be ingredient C. Rozac is produced by blending the 4 chemicals. The cost per pound of each chemical and the amount of each active ingredient in 1 lb of each chemical are given below in the table: Chemical Cost ($ per lb) A B C 1 14 0.07 0.11 0.04 2 11 0.03 0.12 0.01 3 8 0.15 0.13 0.05 4 17 0.09 0.02 0.14 It is necessary that at most 200 lb of chemical 1 are used. Formulate an LP that determines the cheapest way of producing today’s batch of Rozac. (You need to write all the decision variables, objective, and constraints and explain/describe EACH of them in your answer. You do NOT need to write out the parameters in this numerical example.)

Question 1 (30 points) Rohan is putting together a high-ener…

Question 1 (30 points) Rohan is putting together a high-energy trail mix for his next hiking trip. At the grocery store, he can buy three items, peanuts, raisins, and chocolate candies by the ounce for his mix. The items cost $0.4, $0.3, and $0.7 per ounce, respectively. Each ounce of item provides 20, 5, and 6 g grams of protein, and 10, 15, and 35 of sugar, respectively. His mix should include at least 150 g of protein and 100 g of sugar. It should not exceed 600 g of sugar. Formulate a linear program to help Rohan decide the composition of his mix that minimizes cost. (You need to write all the decision variables, objective, and constraints and explain/describe EACH of them in your answer. You do NOT need to write out the parameters in this numerical example.)