The Ace Manufacturing Company has orders for three similar products.
Product Orders (units)
AA 1,800
BB 500
CC 1,400
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)
11 1,600
22 1,500
33 800
Machine
Product
1 2 3
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 x be the number of units of product A produced by machine 1, be the number of units of product i produced by machine j, etc.)
Machine 1 Capacity
Machine 2 Capacity
Machine 3 Capacity
Product A Orders
Product B Orders
Product C Orders
(b) Show the production schedule.
(x A1, x A2, x A3, x B1, x B2, x B3, x C1, x C2, x C3) =
(c) Determine the cost (in dollars) of the production schedule.
Sample Solution