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...st has to be considered at the end of the year in computing the net income. ? XAW - pounds of A-grade tomatoes used to produce whole tomatoes ? XBW - pounds of B-grade tomatoes used to produce whole tomatoes ? XAJ - pounds of A-grade tomatoes used to produce tomato juice ? XBJ - pounds of B-grade tomatoes used to produce tomato juice ? XAP - pounds of A-grade tomatoes used to produce tomato paste ? XBP - pounds of B-grade tomatoes used to produce tomato paste MAXIMIZE 0.0822XAW + 0.0822XBW + 0.066XAJ + 0.066XBJ + 0.074XAP + 0.074XBP SUBJECT TO: QUALITY_WHOLE: XAW - 3.0XBW >= 0 QUALITY_JUICE : 3.0XAJ ? XBJ >= 0 DEMAND_WHOLE: XAW + XBW <= 14400000 DEMAND JUICE: XAJ + XBJ <= 1000000 DEMAND_PASTE: XAP + XBP <= 2000000 AVAILABILITY_A: XAW + XAJ + XAP <= 600000 AVAILABILITY_B: XBW + XBJ + XBP <= 2400000 NONNEG: XAW, XBW, XAJ, XBJ, XAP, XBP >= 0 Since the minimum required average quality point for whole tomatoes is 8 we obtained the quality constraint for the whole tomatoes the following way: (9* XAW + 5* XBW)/ (XAW + XBW) >= 8 which is equivalent to XAW - 3.0XBW >=0 Similarly the quality constraint for tomato juice was modeled. Model solved with BLP. 1.(a) The optimal solution suggests that RBC should produce : - 525,000 lbs (A) + 175,000 lbs (B) = 700,000 lbs/ 18 = 38,888 cases of whole tomatoes. - 75,000 lbs (A) + 225,000 lbs (B) = 300,000 lbs/20 = 15,000 cases of tomato juice - 2,000,000 lbs (B)/25 = 80,000 cases of tomato paste 1. (b) The contribution will be $ 225,340. 1.(c) All the 3,000,000 lbs of tomatoes were used. 1.(d) The average quality point count of the whole tomatoes is 8, of the tomato juice is 6, and the tomato paste is 5 (no slacks in the quality constraints). 1.(e) The worth of one additional pound of A-grade tomatoes is $0.09 1.(f) RBC should buy the extra 80, 000 lbs of A-grade tomatoes@ $0.085 for an additional profit of (0.09 ? 0.085)*80,000 = 0.005*80,000 = $400 2.(a) Problem resolved using Cooper?s contributions figures of $0.4, $0.12 and $0.35 per case of whole tomatoes, juice, and paste correspondingly. According to his solution 600,000lbs of A-grade and 200,000 lbs of B-grade tomatoes should be used to produce whole tomatoes, and 2,000,000 lbs of B-grade tomatoes should be used to produce tomatoes paste. His optimal contribution is $45,760 which is less than the contribution in Part 1. i.e. $225,340. The difference is because Cooper uses the sunk cost in calculating the contributions for each product which is wrong. 2.(b) Problem resolved using Myer?s profit figures of $0.01, $0.08 and $0.55 per case of whole tomatoes, juice, and paste correspondingly. His solution suggests that 250,000 lbs ...