The Ace Manufacturing Company has orders for three similar products. Product A Min B C 1 2 Machine 3 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 A C B с с 1 Product 12 3 Orders (units) 1,900 500 1,100 Capacity (units) 1,300 1,600 800 1 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20 (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.) Machine 2 3

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The Ace Manufacturing Company has orders for three similar products.
Product
A
Min
B
C
1
2
Machine
3
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.
A
A
B
B
Ic
C
Product
1
12
3
Orders
(units)
1,900
500
1,100
Capacity
(units)
1,300
1,600
800
1
Machine
2
3
$1.00 $1.30 $1.10
$1.20 $1.40 $1.00
$0.90 $1.20 $1.20
(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.)
Transcribed Image Text:The Ace Manufacturing Company has orders for three similar products. Product A Min B C 1 2 Machine 3 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. A A B B Ic C Product 1 12 3 Orders (units) 1,900 500 1,100 Capacity (units) 1,300 1,600 800 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20 (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.)
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, XC₂₁ XC3) = 1
Determine the cost (in dollars) of the production schedule.
Total = $
Transcribed Image Text: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, XC₂₁ XC3) = 1 Determine the cost (in dollars) of the production schedule. Total = $
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