The Ace Manufacturing Company has orders for three similar products. Product A B C 1 2 Machine 3 A A 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. B B U C с Product 2 3 Orders (units) 2,400 500 1,400 Capacity (units) 1,800 1,800 1,100 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20
The Ace Manufacturing Company has orders for three similar products. Product A B C 1 2 Machine 3 A A 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. B B U C с Product 2 3 Orders (units) 2,400 500 1,400 Capacity (units) 1,800 1,800 1,100 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section: Chapter Questions
Problem 67P
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Transcribed Image Text:The Ace Manufacturing Company has orders for three similar products.
Product
A
B
C
1
2
Machine
3
A
A
B
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.
B
C
Product
C
2
Orders
(units)
3
2,400
500
1,400
Capacity
(units)
1,800
1,800
1,100
1
Machine
2
3
$1.00 $1.30 $1.10
$1.20 $1.40 $1.00
$0.90 $1.20 $1.20
Transcribed Image Text:Xij
(a) Develop the linear programming formulation of this problem. (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.)
Min
s.t.
Machine 1 Capacity
Machine 2 Capacity
Machine 3 Capacity
Product A Orders
Product B Orders
Product C Orders
Xij ≥ 0 for all i, j.
||||||
(b) Solve the transportation model for the minimum cost production schedule for the products and machines.
Show the production schedule.
(XA1, XA2 XA3, XB1, XB2, XB3, XC1, XC2, XC3)
Total
=
Determine the cost (in dollars) of the production schedule.
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