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. gloves produced TCD(X)=x²-x+ 3 where X is the weekly production volume in thousands units and TCD(X) is the cost in thousands of dollars. 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 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 produce each week each facility. X²-X+4+ y² + 2Y+5 min s.t. X+Y X, Y Z 0 X (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)? $ 26000 3000,2000 at (X,Y)=
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. gloves produced TCD(X)=x²-x+ 3 where X is the weekly production volume in thousands units and TCD(X) is the cost in thousands of dollars. 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 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 produce each week each facility. X²-X+4+ y² + 2Y+5 min s.t. X+Y X, Y Z 0 X (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)? $ 26000 3000,2000 at (X,Y)=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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 + 3
where 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 by
TCH(Y) = y² + 2Y + 9
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 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.
X²-X+4+ y² + 2Y+5
min
s.t.
X + Y
X, Y Z 0
= 5
X
(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)?
$ 26000
3000,2000
at (x, y) =
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