and Super (s L2R 1 65 s 600 assembly (hours 0SR ?.ss s 300 paint (hours) 0368 0.
ID: 434743 • Letter: A
Question
and Super (s L2R 1 65 s 600 assembly (hours 0SR ?.ss s 300 paint (hours) 0368 0.45 S 100 inspection (hours Compater Soleticn Sensitivity Report Cell 5857 Final Shadow Coastraint Alowable Allowable Valve Price R.H. Side crease Cell SESS SES4 Paint (hrunit) 175 300.00 100.00 3333 300 Fill the following blanks: a) and the o The optimal number of Regular (R) products to produce is number of Super (S) products to produce is for total profits of b) If the company wanted to increase the available hours for one of their (assembly, painting, or inspection) by 2 hours, they should increase c) The profit on the super product could increase by without affecting the product mix If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would be reduced by d) A change in the market has increased the profit on the super product by $5. Total profit will increase by_ e) meExplanation / Answer
Answers are provided first followed by the explanation. You may choose to ignore the explanation while answering.
a) Optimal number of regular products to produce is 291.67 and the optimal number of super products to produce is 133.33 for total profit of (50*291.67 + 75*133.33) = 24583.25. The final values for Regular and Super rows provide the values of R and S respectively. Use them in the objective function to receive the total profit.
b) If the company wanted to increase the available hours for one of their constraints by 2 hours, they should increase “Inspect”. In the constraint table, the shadow price of Inspect is the highest. This means for every unit increase of inspect the optimal solution value will increase by that shadow price value. By increasing inspect by 2 hours, we will gain 2*145.83 = 291.66 addition into the optimal solution.
c) The profit on super product could increase by 50 without affecting the product mix. The product mix is the value of R and S. We see that the allowable increase for Super is 50. Thus as long as we increase it up to that limit, the product mix will remain the same.
d) If downtime reduced the available capacity for painting by 40 hours, profit would be reduced by 40*33.33 = 1333.2. The shadow price indicated the change in optimal value due to change of 1 unit in the final value for a constraint.
e) A change in the market has increased the profit on the super product by $5. Total profit will increase by 5*133.33 = 666.65. The increase of $5 is within the allowable increase for Super. Thus the product mix will not change. However, the total profit will be impacted due to the change in profit value.
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