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The Ace Manufacturing Company has orders for three similar products. Product Orders ( units ) A A 1 , 9 0 0 B B 4

The Ace Manufacturing Company has orders for three similar products.
Product Orders
(units)
A A 1,900
B B 400
C C 1,300
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 Capacity
(units)
111,400
221,400
33900
Machine
Product 123
A $1.00 $1.30 $1.10
B $1.20 $1.40 $1.00
C $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,
xij
be the number of units of product i produced by machine j, etc.)
Min xA1+1.3xA2+1.1xA3+1.2xB1+1.4xB2+xB3+0.90xC1+1.2xC2+1.2xC3
s.t.
Machine 1 Capacity xA1+xB1+xC1<=1400
Machine 2 Capacity xA2+xB2+xC2<=1400
Machine 3 Capacity xA3+xB3+xC3<=900
Product A Orders xA1+xA2+xA3=1900
Product B Orders xB1+xB2+xB3=400
Product C Orders xC1+xC2+xC3=1300
xij >=0 for all i, j.
(b)
Show the production schedule.
(xA1, xA2, xA3, xB1, xB2, xB3, xC1, xC2, xC3)=
1400,1400,
(c)
Determine the cost (in dollars) of the production schedule.
Total = $

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