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 Bean 1 Bean 2 Bean 3 2 3 Bean 1 2 3 $0.50 $0.70 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 $0.45 240 435 325 75 85 60 85 x lb x lb 87 450 74 550 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? x lb 350 (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 x (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 Bean 1 Bean 2 Bean 3 2 3 Bean 1 2 3 $0.50 $0.70 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 $0.45 240 435 325 75 85 60 85 x lb x lb 87 450 74 550 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? x lb 350 (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 x (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
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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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