Use the transportation model to develop the minimum cost production schedule for the products and machines. (a) Show the linear programming formulation. (Let X; be the number of units of product A produced by machine 1, xy be the number of units of product / produced by machine J, etc.) Min s.t. Machine 1 Capacity Machine 2 Capacity Machine 3 Capacity Product A Orders Product B Orders Product C Orders xy 0 for all i, J. (b) Show the production schedule. (XA1 A2 A3 *81*62*83*c*ca ·xaxa) - (c) Determine the cost (in dollars) of the production schedule. Total = $

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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The Ace Manufacturing Company has orders for three similar products.
Orders
(units)
Product
Min
A
s.t.
B
с
1
Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week
and the unit costs are shown below.
Machine
2
3
LB
A
C
B
с
1
Product
112₂
3
Machine 1 Capacity
Machine 2 Capacity
Machine 3 Capacity
2,200
Product A Orders
Product C Orders
400
xij≥0 for all i, j.
1,400
Product B Orders
Capacity
(units)
1,500
1,500
Use the transportation model to develop the minimum cost production schedule for the products and machines.
(a) Show the linear programming formulation. (Let XA1 be the number of units of product A produced by machine 1, X;; be the number of units of product i produced by machine j, etc.)
1,100
$1.00 $1.30 $1.10
1
$1.20 $1.40 $1.00
Machine
2
3
$0.90 $1.20 $1.20
(b) Show the production schedule.
(XA1, XA2, XA3, XB1, XB2, XB3, XC1, XC2, XC3) =
(c) Determine the cost (in dollars) of the production schedule.
Total = $
Transcribed Image Text:The Ace Manufacturing Company has orders for three similar products. Orders (units) Product Min A s.t. B с 1 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. Machine 2 3 LB A C B с 1 Product 112₂ 3 Machine 1 Capacity Machine 2 Capacity Machine 3 Capacity 2,200 Product A Orders Product C Orders 400 xij≥0 for all i, j. 1,400 Product B Orders Capacity (units) 1,500 1,500 Use the transportation model to develop the minimum cost production schedule for the products and machines. (a) Show the linear programming formulation. (Let XA1 be the number of units of product A produced by machine 1, X;; be the number of units of product i produced by machine j, etc.) 1,100 $1.00 $1.30 $1.10 1 $1.20 $1.40 $1.00 Machine 2 3 $0.90 $1.20 $1.20 (b) Show the production schedule. (XA1, XA2, XA3, XB1, XB2, XB3, XC1, XC2, XC3) = (c) Determine the cost (in dollars) of the production schedule. Total = $
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