(this is one exercise)

2. A hospital laundry has decided to become ecological and desires to manufacture its own pollution-free detergent of which it uses 300 lb. per week. It has been found that for greatest cleaning efficiency in these detergents, they must contain 2/3 pentaerythritol monolkonates (200 lb., for this hospital) and 1/3, monoglycerides (100 lb, for this hospi- tal). These ingredients are available in bulk from the following companies in the follow- ing proportions: Pentaerythritol Monoglyceride Company Monolkonate Cost (%) 80 Alpha (a) Beta (6) 20 50 $0.20/ib $0.15/ 50 How much detergent should be purchased from each company to minimize the cost of manufacture? Formulate as a linear program (do not solve). Find 1. One of the decision variables is the quantity of: a. monoglyceride b. beta. c. detergent manufactured. d. both band e. All 2. The objective function is: a. min. 300 (alpha+beta) b. max. amount of detergent produced c. min 20(alpha) + 15 (beta) d. min. (Pent. Mono. + Monogl.), cost of, 3. Assume the following notations: x = quantity of alpha, xb = Tantity of beta, * - quantity of Penta Mono, X = quantity of Monogl. The constraint that ex- presses the cleaning efficiency is 2. 2/3x + 1/3xd >_300 b. 100x + 200x3 = 300 C. 8x + 2x > 200 d. 2x + 5x>-100 e. none of above 3. Given: Objective Maximize PC - 3X + 7 S.T. 2X + 2Y = 16 10x+10Y 300 2X Y X 20 Y=0 3. Given: Objective Maximize PC = 3X + ZY S.T. 2X + 2Y = 16 10x + 10Y S 300 2X 2 Y X 20; Y 20 a. Shade the feasible space on the graph below. b. Circle the optimal solution. c. Explain clearly in werds, why you circled the point below