A Steel Manufacturing company has two production facilities that manufacture Dishwashers. Production costs at the two facilities differ because of varying labor costs, local property taxes, type of material used, volume, and so on. For Plant A, the weekly costs for producing a number of units of Dishwashers is expressed as a function:
TCA(X) = X2 - 2X + 12000 where X is the weekly production volume and TCA(X) is the weekly cost for Plant A.
Plant B’s weekly production costs are given by TCB(Y) = Y2 + 8Y + 10000 where Y is the weekly production volume and TCB(Y) is the weekly cost for Plant B. The manufacturer would like to produce 50 dishwashers per week at the lowest possible cost.
a. Formulate a mathematical model that can be used to determine the optimal number of dishwashers to produce each week at each facility.
b. Solve the optimization model to determine the optimal number of dishwashers to produce at each facility.