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3) The Sunshine Food Processing Company produces three canned fruit products—mixed fruit (X1), fruit cocktail (X2), and fruit delight (X3). The main ingredients in each product are pears and peaches. Each product is produced in lots and must go through three processes—mixing, canning, and packaging. The resource requirements for each product and each process are shown in the following linear programming formulation.Max Z = 10X1+ 6X2+ s.t. 20X1+ 10X2+ 16X3 320 (pears, lb)10X1+ 20X2+ 16X3 400 (peaches, lb)1X1+ 2X2+ 2X3 43 (mixing, hr)1X1+ 1X2+ 1X3 60 (canning, hr)2X1+ 1X2+ 1X3 40 (packaging, hr)X1, X2,X308X3
a.Solve the problem using Excel. Be sure to obtain the sensitivity report when you solve.
b. What is the maximum price the company would be willing to pay for additional pears?$0.467 per lb. How much could be purchased at that price? 80 lbs.c.What is the marginal value of peaches? $0.067 per lb.Over what range is this price valid?160 <b2<430d.The company can also purchase a new mixing machine that would increase the available mixing time from 43 to 60 hours. Would this affect the optimal solution?No because you already have unused hoursmixing.
e.The company can also purchase a new packaging machine that would increase the available packaging time from 40 to 50 hours.