In the product mix example in this chapter, Quick-Screen is considering adding some extra operators who would reduce processing times for each of the four clothing items by 10%. This would also increase the cost of each item by 10% and thus reduce unit profits by this same amount (because an increase in selling price would not be possible). Can this type of sensitivity analysis be evaluated using only original solution output, or will the model need to be solved again? Should Quick-Screen undertake this alternative?
In this problem, the profit per shirt is computed from the selling price less fixed and variable costs. The computer solution output shows the shadow price for T-shirts to be $4.11. If Quick-Screen decided to acquire extra T-shirts, could the company expect to earn an additional $4.11 for each extra T-shirt it acquires above 500, up to the sensitivity range limit of T-shirts? If Quick-Screen produced equal numbers of each of the four shirts, how would the company reformulate the linear programming model to reflect this condition? What is the new solution to this reformulated model?