Practice Problems - Sensitivity Analysis .pdf - BU275 Practice Problems for Linear Programming What-if Analysis Problem 1 Fashion Designs produces four

Practice Problems - Sensitivity Analysis .pdf - BU275...

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BU275: Practice Problems for Linear Programming – What-if Analysis Problem 1 Fashion Designs produces four clothing products – pants, dresses, skirts and blouses. The company needs to make at least 300 garments in total. Further, the number of blouses produced should be more than the number of skirts by at least 20. The firm has 800 hours of cutting time, 720 hours of sewing time and 600 hours of packing and inspecting time. Each pant requires 1 hour of cutting time, 4 hours of sewing time and 2 hours of packing and inspecting time. Each dress requires 1 hour of cutting time, 2 hours of sewing time and 2 hours of packing and inspecting time. Each skirt requires 4 hours of cutting time, 1 hour of sewing time and 1 hour of packing and inspecting time. Each blouse requires 1 hour of cutting time, 3 hours of sewing time and 1 hour of packing and inspecting time. The profit from a pant, dress, skirt and blouse are respectively $15, $16, $12 and $16. LP Formulation Decision Variables P - # of pants to produce D - # of dresses to produce S - # of skirts to produce B - # of blouses to produce Objective function Maximize z = 15P + 16D + 12S + 16B Constraints Cutting: P + D + 4S + B < 800 Sewing: 4P + 2D + S + 3B < 720 Packing & Inspect: 2P + 2D + S + B < 600 Min. production: P + D + S + B > 300 Blouse & skirt: B > S + 20 P,D,S,B > 0 The sensitivity report for the problem is given below.
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Each statement below refers to the original problem. In other words, each statement is independent of other statements. For each statement given below determine if the optimal solution changes or not. Also determine if the objective function value (OFV) is unchanged or not. If the OFV changes determine the new OFV if you can, otherwise, say that you need to re-solve the problem to obtain the new OFV. Give reasons for your answers. a. Profit per pant increases to $25. b. Profit per dress decreases to $14. c. Profit per blouse decreases by $3 and profit per skirt increases by $2. d. Profit per skirt decreases by $3 and profit per blouse increases by $2. e. Only 600 hours are available in the cutting department f. Only 690 hours are available in the packing department g. Have to produce at least 50 more blouses than skirts h. There are only 500 hours available in cutting. Also the minimum number of garments that must be produced is 350. i. The company has decided that there is no minimum number of garments they need to produce. j. The company has unlimited availability for packing. In other words you can get as many hours of packing as you need (theoretically infinite).
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  • Winter '13
  • HosseinZolfagharinia

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