A Steel Manufacturing Company Has Two Production Facilities That Manufacture

Essay

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
TC_A(X) = X² - 2X + 12000
where X is the weekly production volume and TC_A(X) is the weekly cost for Plant A. Plant B's weekly production costs are given by
TC_B(Y) = Y² + 8Y + 10000
where Y is the weekly production volume and TC_B(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.