Case 4.2 of Decision Analysis

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Case 4.2 a. The weekly product mix should consist of 700 ballpoint pens and 133 fountain pens. The weekly net profit is $2765. b. The optimal solution to question 1 is not degenerate, because the allowable increase or decrease on any constraint is not zero. c. The optimal solution from question 1 is unique, because the values in the allowable Increase or allowable decrease columns for the Changing Cells are not zero. d. The shadow price for chrome is $0 per ounce and the maximum allowable increase is 1E+30 ounces. Because 1 is in this range, the $0 is valid. Thus, the value of 1 additional ounce is = 1($0) = $0. The shadow price for plastic is $1.167 per ounce and the maximum allowable increase is 200 ounces. Because 1 is in this range, the $1.167 is valid. Thus, the value of 1 additional ounce is = 1 ($1.167) = $1.167. e. The company should buy the steel at this price. The shadow price for stainless steel is $0.8 per ounce and the maximum allowable increase is 555.6 ounces. Because 500 is in this range, the $0.8 is valid. Thus, the value of 500 additional ounces is = 500 ($0.8) = $400. However, the local distributor has offered to sell Parket Sisters an additional 500 ounces of stainless steel for $0.60 per ounce more than it ordinarily pays, so the value of 500 additional ounces is =500(0.8)- 500 ($0.6) = $100>0. f. An increase of 500 in the RHS value of the third constraint is within the allowable range of increase for the shadow price of this constraint. Therefore, if the RHS for the third constraint increases from 2000 to 2500, and the local distributor has offered to sell Parket Sisters an additional 500 ounces of stainless steel for $0.60 per ounce more than it ordinarily pays, the new optimal profit would be approximately 2765 + 0.8 *500-0.6*500=2865. The new optimal product mix should consist of ballpoint

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