Fall 2017 b) Sensitivity report for Telson problem is given below. Use this repo
ID: 378015 • Letter: F
Question
Fall 2017 b) Sensitivity report for Telson problem is given below. Use this report to answer the following questions. Show your work Variable Cells Final Reduced Objective Allowable Allowable Value Cost Coefficient Increas Decrease Cell SC$3 Regular SD$3 Catcher's Name 500 150 4.67 Constraints Final Shadow Constraint Cell SES7 Cutting & Sewing LHS SES8 Finishing LHS SES9 Packaging & Shipping LHS 725 300 900 1E+30 300 100 35 175 166.67 25 100 28 100 >w Vhat are the optimal solution and optimal value? What would be the optimal solution and optimal value when the profit of Catcher's model becomes $9? i) Because of the increased competition, Telson is considering reducing the price of Regular model such that new profit is $4 per unit. How would this change in price affect the optimal solution and optimal value? Explain. iv) Suppose that available hours in finishing department is reduced from 300 to 200. How would this change affect the optimal value? Explain. v) If Telson has an option to increase its packaging& shipping by 900 minutes with a total cost of $360, should they do that? Why? Explain.Explanation / Answer
i) Read from the sensitivity report, final values
Regular = 500
Catcher's = 150
Optimal value =500*5 (coefficient) + 150*8 = 3700
ii) change from 8 to 9 is 1. Allowable increase is 2 , therefore this is within allowable range. Hence optimal solution remains unchanged. New Total profit = 500*5+150*9 = 3850
iii) Allowable decrease of Regular model 1, therefore reduction from 5 to 4 is within allowable range. Therefore optimal solution will remain unchanged. Optimal value will reduce by 500
New Optimal value = 500*4 + 150*8 = 3200
iv) allowable decrease of finishing is 166.67 , therefore reduction from 300 to 200 is within allowable range. therefore shadow price of 3 is applicable in this range. optimal value will decrease by 3*100 = 300
New optimal value = 3700-300 = 3400
v) 900 minutes is 15 hours. allowable increase is 35 . therefore it is within allowable range. therefore shadow price applies. increase in optimal value = 15*28 = 420
cost of 360 is less than increase in profit. therefore this deal is profitable. They should do that
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