The Sunshine Food Processing Company produces three canned fruit products: mixed fruit (r1), fruit cocktail (x2),...

 

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The Sunshine Food Processing Company produces three canned fruit products: mixed fruit (r1), fruit cocktail (x2), and fruit delight (r3). The main ingredients in each product are pears and peaches. Each product is produced in lots and must go through two processes: mixing and canning. The resource requirements for each product and each process are given in the following LP formulation: max z= 4x1 + 10.r2 + 8r3 (profit) < 200 (pears, kg) < 160 (peaches, kg) < 50 (mixing, hr) < 80 (canning, hr) %3D s.t. 5r1 + 4r2+4r3 2.r1 + 5x2 + 2r3 I1 +x2 + 2r3 2.x1 + 4r2 + 2.r3 *1, 12, 13 20 The optimal Simplex Tableau is as follows: S2 S3 S4 RHS 260 80 2 1 3 1 70 3 3 - 20 1 1 10 3 a. (5 pts) What is the marginal value of an additional hour of mixing? Over what range is this value valid? b. (5 pts) Given a choice between securing more mixing hours or more canning hours, which should management select? Why? c. (10 pts) What unit profit would have to be made from mixed fruit before management would consider producing it? d. (10 pts) Management is considering changing the profit of fruit delight from 8 TL to 13 TL. What will be the new optimal solution and profit? a - -l The Sunshine Food Processing Company produces three canned fruit products: mixed fruit (r1), fruit cocktail (x2), and fruit delight (r3). The main ingredients in each product are pears and peaches. Each product is produced in lots and must go through two processes: mixing and canning. The resource requirements for each product and each process are given in the following LP formulation: max z= 4x1 + 10.r2 + 8r3 (profit) < 200 (pears, kg) < 160 (peaches, kg) < 50 (mixing, hr) < 80 (canning, hr) %3D s.t. 5r1 + 4r2+4r3 2.r1 + 5x2 + 2r3 I1 +x2 + 2r3 2.x1 + 4r2 + 2.r3 *1, 12, 13 20 The optimal Simplex Tableau is as follows: S2 S3 S4 RHS 260 80 2 1 3 1 70 3 3 - 20 1 1 10 3 a. (5 pts) What is the marginal value of an additional hour of mixing? Over what range is this value valid? b. (5 pts) Given a choice between securing more mixing hours or more canning hours, which should management select? Why? c. (10 pts) What unit profit would have to be made from mixed fruit before management would consider producing it? d. (10 pts) Management is considering changing the profit of fruit delight from 8 TL to 13 TL. What will be the new optimal solution and profit? a - -l