A linear programming computer package is needed. Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are as follows. Bean Cost per Pound Available Pounds 1 2 3 Bean 1 2 3 $0.50 Consumer tests with coffee products were used to provide ratings on a scale of 0-100, with higher ratings Indicating higher quality. Product quality standards for the blended coffee require a consumer rating for aroma to be at least 75 and a consumer rating for taste to be at least 80. The Individual ratings of the aroma and taste for coffee made from 100% of each bean are as follows: Aroma Rating Taste Rating $0.70 $0.45 240 435 325 75 85 60 85 87 450 74 550 350 Assume that the aroma and taste attributes of the coffee blend will be a weighted average of the attributes of the beans used in the blend. (a) What is the minimum-cost blend (In pounds) that will meet the quality standards and provide 1,000 pounds of the blended coffee product? Bean 1 x lb Bean 2 x lb Bean 3 x lb (b) What is the cost per pound for the coffee blend (in dollars)? $0.604 x (c) Determine the aroma rating for the coffee blend. 78.675 Determine the taste rating for the coffee blend. 80.025 (d) If additional coffee were to be produced, what would be the expected cost per pound (in dollars)? $
A linear programming computer package is needed. Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are as follows. Bean Cost per Pound Available Pounds 1 2 3 Bean 1 2 3 $0.50 Consumer tests with coffee products were used to provide ratings on a scale of 0-100, with higher ratings Indicating higher quality. Product quality standards for the blended coffee require a consumer rating for aroma to be at least 75 and a consumer rating for taste to be at least 80. The Individual ratings of the aroma and taste for coffee made from 100% of each bean are as follows: Aroma Rating Taste Rating $0.70 $0.45 240 435 325 75 85 60 85 87 450 74 550 350 Assume that the aroma and taste attributes of the coffee blend will be a weighted average of the attributes of the beans used in the blend. (a) What is the minimum-cost blend (In pounds) that will meet the quality standards and provide 1,000 pounds of the blended coffee product? Bean 1 x lb Bean 2 x lb Bean 3 x lb (b) What is the cost per pound for the coffee blend (in dollars)? $0.604 x (c) Determine the aroma rating for the coffee blend. 78.675 Determine the taste rating for the coffee blend. 80.025 (d) If additional coffee were to be produced, what would be the expected cost per pound (in dollars)? $
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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Ee 418.
Transcribed Image Text:A linear programming computer package is needed.
Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are as follows.
Bean Cost per Pound Available Pounds
1
2
3
1
$0.50
$0.70
2
$0.45
3
Consumer tests with coffee products were used to provide ratings on a scale of 0-100, with higher ratings Indicating higher quality. Product quality standards for the blended coffee require a consumer rating for aroma to be at least 75 and a consumer rating for taste to be at least 80. The
Individual ratings of the aroma and taste for coffee made from 100% of each bean are as follows:
Bean Aroma Rating Taste Rating
75
85
60
85
450
87
550
74
350
Assume that the aroma and taste attributes of the coffee blend will be a weighted average of the attributes of the beans used in the blend.
(a) What is the minimum-cost blend (In pounds) that will meet the quality standards and provide 1,000 pounds of the blended coffee product?
Bean 1
240
Xlb
Bean 2
435
x lb
Bean 3 325
Xlb
(b) What is the cost per pound for the coffee blend (in dollars)?
$ 0.604
x
(c) Determine the aroma rating for the coffee blend.
78.675
X
Determine the taste rating for the coffee blend.
80.025
x
(d) If additional coffee were to be produced, what would be the expected cost per pound (in dollars)?
$
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