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 weeklycosts that can be expressed as a function of the number of gloves producedTCD(X) = X² X + 3where X is the weekly production volume in thousands of units and TCD(X) is the cost in thousands of dollars. The Hamilton plant's weekly production costs are given byTCH(Y)y² + 2Y + 9where 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 5,000 gloves per week at the lowest possible cost.(a) Formulate a mathematical model that can be used to determine the optimal number of gloves to produce each week at each facility.mins.t.=X, Y Z 0= 5(b) 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. What is the optimal solution value (in dollars)?at (x, y) =$

Here, in the question, it is given a Hellar manufacturing plant that 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+3 The Hamilton plant's weekly production costs are given by: TCH(Y) = Y2+2Y+9 where Y is the weekly production volume in thousands of units and TCD(x) is the cost in thousand of dollars. This a question of mixed linear programming and also mathematical modeling. We have to find out the respective equations to find out the basic feasible solution. The formulation is required to be done.The mathematical model is to develop a minimum weekly total cost function. Objective Function( Minimization) = TCD(X) + TCH(Y) Constraints are" X+Y≥5 ( Here 5 is because volumes are expressed in thousands in the function) X, Y>=0 We can use the solver parameters and equations to solve the equation: Here, if we consider X, Y are the variables given in thousand units the cost function is in thousand $. Production in Dayton Plant = 3000 units Production in Hamilton Plant = 2000 units Therefore putting the values cost will be: 32-3+3+4+4+9=26 Total cost will be: $26000