Heller Manufacturing has two production facilities that manufacture baseball gloves. Production costs at the two facilities differ because of varying labor rates, local property taxes, type of equipment, capacity, and so on. The Dayton plant has weekly costs that can be expressed as a function of the number of gloves produced:

TCD(X) = X² X + 7

where X is the weekly production volume in thousands of units and TCD(X) is the cost in thousands of dollars. The Hamilton plants weekly production costs are given by

TCH(Y) = Y² + 2Y + 5

where Y is the weekly production volume in thousands of units and TCH(Y) is the cost in thousands of dollars. Heller Manufacturing would like to produce 8000 gloves per week at the lowest possible cost.

1. Formulate a mathematical model that can be used to determine the optimal number of gloves to produce each week at each facility. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. If the constant is "1" it must be entered in the box.

   maxmin	fill in the blank 2 X2 + fill in the blank 3 X + fill in the blank 4 + fill in the blank 5 Y2 + fill in the blank 6 Y + fill in the blank 7
   s.t.
   	fill in the blank 8 X + fill in the blank 9 Y =<> fill in the blank 11
   	X, Y 0

2. Use Excel Solver or LINGO to find the solution to your mathematical model to determine the optimal number of gloves to produce at each facility. If required, round your answers to two decimal places. The optimal solution is X = fill in the blank 12 and Y = fill in the blank 13 for an optimal objective value of $ fill in the blank 14.