Problem 6-09 (Algorithmic)

The Ace Manufacturing Company has orders for three similar products:

Product	Order (Units)
A	2250
B	550
C	1100

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 as follows:

Machine	Capacity (Units)
1	1550
2	1600
3	1150

	Product
Machine	A	B	C
1	$1.10	$1.30	$0.70
2	$1.40	$1.40	$1.40
3	$0.90	$0.80	$1.50

Use the transportation model to develop the minimum cost production schedule for the products and machines. Show the linear programming formulation. If the constant is "1" it must be entered in the box. If your answer is zero enter "0".

The linear programming formulation and optimal solution are shown.

Let x_ij = Units of product j on machine i.

Min

x1A

+

x1B

+

x1C

+

x2A

+

x2B

+

x2C

+

x3A

+

x3B

+

x3C

s.t.

x1A

+

x1B

+

x1C

x2A

+

x2B

+

x2C

x3A

+

x3B

+

x3C

x1A

+

x2A

+

+

x3A

=

x1B

+

x2B

+

x3B

=

x1C

+

x2C

+

x3C

=

xij 0 for all i, j

If required, round your answers to the nearest whole number.

Optimal Solution	Units	Cost
1-A		$
1-B		$
1-C		$
2-A		$
2-B		$
2-C		$
3-A		$
3-B		$
3-C		$
		Total $