A coffee manufacturer blends four component coffee beans into three final blends of coffee. The table below summarises the very precise recipes for the final coffee blends, the cost and availability information for the four components, and the wholesale price per pound of the final blends. The percentages in the body of the table indicate the percentage of each component to be used in each blend.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Problem 6:
A coffee manufacturer blends four component coffee beans into three final blends of
coffee. The table below summarises the very precise recipes for the final coffee blends,
the cost and availability information for the four components, and the wholesale price
per pound of the final blends. The percentages in the body of the table indicate the
percentage of each component to be used in each blend.
Component
1
2
3
4
Wholesale
price per
pound
Final Blend (%)
2
1
20
40
15
25
35
15
20
30
3
10
35
40
15
OR1.25 OR1.5 OR1.4
Cost per
pound (OR)
0.60
0.80
0.55
0.70
Maximum
availability each
week (pounds)
40000
25000
20000
45000
wishes to
Weekly capacity for the processor's plant is 100000 pounds, and the company
operate at full capacity. There is no problem in selling the final blends, although there is
a requirement that minimum production levels of 10000, 25000, and 30000 pounds,
respectively, be met for blends 1, 2, and 3. Determine the number of pounds of each
component, which should be used in each blend so as to maximise total weekly profit.
Transcribed Image Text:Problem 6: A coffee manufacturer blends four component coffee beans into three final blends of coffee. The table below summarises the very precise recipes for the final coffee blends, the cost and availability information for the four components, and the wholesale price per pound of the final blends. The percentages in the body of the table indicate the percentage of each component to be used in each blend. Component 1 2 3 4 Wholesale price per pound Final Blend (%) 2 1 20 40 15 25 35 15 20 30 3 10 35 40 15 OR1.25 OR1.5 OR1.4 Cost per pound (OR) 0.60 0.80 0.55 0.70 Maximum availability each week (pounds) 40000 25000 20000 45000 wishes to Weekly capacity for the processor's plant is 100000 pounds, and the company operate at full capacity. There is no problem in selling the final blends, although there is a requirement that minimum production levels of 10000, 25000, and 30000 pounds, respectively, be met for blends 1, 2, and 3. Determine the number of pounds of each component, which should be used in each blend so as to maximise total weekly profit.
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