Answered: Optimal Solution Units Cost 1-A fill in…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

The Ace Manufacturing Company has orders for three similar products:

Product	Order (Units)
A	1750
B	500
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	1450
3	1150

	Product
Machine	A	B	C
1	$0.80	$1.30	$0.70
2	$1.40	$1.30	$1.50
3	$0.80	$0.80	$1.20

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

fill in the blank 1x_1A

fill in the blank 2x_1B

fill in the blank 3x_1C

fill in the blank 4x_2A

fill in the blank 5x_2B

fill in the blank 6x_2C

fill in the blank 7x_3A

fill in the blank 8x_3B

fill in the blank 9x_3C

s.t.

fill in the blank 10x_1A

fill in the blank 11x_1B

fill in the blank 12x_1C

≤

fill in the blank 13

fill in the blank 14x_2A

fill in the blank 15x_2B

fill in the blank 16x_2C

≤

fill in the blank 17

fill in the blank 18x_3A

fill in the blank 19x_3B

fill in the blank 20x_3C

≤

fill in the blank 21

fill in the blank 22x_1A

fill in the blank 23x_2A

fill in the blank 24x_3A

fill in the blank 25

fill in the blank 26x_1B

fill in the blank 27x_2B

fill in the blank 28x_3B

fill in the blank 29

fill in the blank 30x_1C

fill in the blank 31x_2C

fill in the blank 32x_3C

fill in the blank 33

x_ij ≥ 0 for all i, j

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

Optimal Solution	Units	Cost
1-A	fill in the blank 34	$ fill in the blank 35
1-B	fill in the blank 36	$ fill in the blank 37
1-C	fill in the blank 38	$ fill in the blank 39
2-A	fill in the blank 40	$ fill in the blank 41
2-B	fill in the blank 42	$ fill in the blank 43
2-C	fill in the blank 44	$ fill in the blank 45
3-A	fill in the blank 46	$ fill in the blank 47
3-B	fill in the blank 48	$ fill in the blank 49
3-C	fill in the blank 50	$ fill in the blank 51
		Total $ fill in the blank 52

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