Orders Product (units) A B с Machine 1 2 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. 3 A A Product B с с G s.t. Machine 1 Capacity Machine 2 Capacity Machine 3 Capacity 2,100 Product A Orders 700 Product B Orders xij z 0 for all i, j. 1,200 Product C Orders Capacity (units) 1,400 1,400 1.400 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 1 $0.90 $1.20 $1.20 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 / produced by machine J, etc.) Min Machine 2 3 (b) Show the production schedule. (XA1 XA2 A3 XB1 *82 XB3XC1 XC2 XC3) - ( (c) Determine the cost (in dollars) of the production schedule.
Orders Product (units) A B с Machine 1 2 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. 3 A A Product B с с G s.t. Machine 1 Capacity Machine 2 Capacity Machine 3 Capacity 2,100 Product A Orders 700 Product B Orders xij z 0 for all i, j. 1,200 Product C Orders Capacity (units) 1,400 1,400 1.400 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 1 $0.90 $1.20 $1.20 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 / produced by machine J, etc.) Min Machine 2 3 (b) Show the production schedule. (XA1 XA2 A3 XB1 *82 XB3XC1 XC2 XC3) - ( (c) Determine the cost (in dollars) of the production schedule.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Question
Transcribed Image Text:The Ace Manufacturing Company has orders for three similar products.
Product
Min
A
s.t.
B
C
1
Machine
2
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.
3
A
A
B
Product
B
с
4
2
3
Machine 1 Capacity
Machine 2 Capacity
Machine 3 Capacity
Product A Orders
Product B Orders
Orders
(units)
Product C Orders
2,100
≥ 0 for all i, j.
700
1,200
Capacity
(units)
1,400
1,400
1,400
1
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.)
Xij
Machine
2
$1.00 $1.30
$1.20 $1.40
3
$1.10
$1.00
$0.90 $1.20 $1.20
(b) Show the production schedule.
(XA1¹ XA2 XA3, XB1¹ XB2¹ XB3¹ XC1¹ XC2₁ XC3) =
(c) Determine the cost (in dollars) of the production schedule.
Total = $
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