A bakery gets milk from two dairies then blends the milk to get the desired amount of butterfat for use in the company's best selling product. Milk from dairy I costs $2.10 per gallon, and milk from dairy Il costs $0.70 per gallon. The company has at most $140 available for purchasing milk. Dairy I can supply at most 54 gallons of milk averaging 3.8% butterfat and dairy II can supply at most 88 gallons of milk averaging 3.2% butterfat. The blend can contain no more than 100 gallons of milk and should contain the maximum amount of butterfat. (a) Let x be the number of gallons of milk from dairy I and let y be the number of gallons of milk from dairy II. State the objective function. Maximize z = (b) Excluding nonnegativity constraints, how many constraints are needed for this model? (b) How much milk from each dairy should the bakery use? Round your answers to the nearest integer as needed. gallons from dairy I and gallons from dairy II. (c) What is the maximum amount of butterfat? Round your answer to two decimal places as needed. gallons
A bakery gets milk from two dairies then blends the milk to get the desired amount of butterfat for use in the company's best selling product. Milk from dairy I costs $2.10 per gallon, and milk from dairy Il costs $0.70 per gallon. The company has at most $140 available for purchasing milk. Dairy I can supply at most 54 gallons of milk averaging 3.8% butterfat and dairy II can supply at most 88 gallons of milk averaging 3.2% butterfat. The blend can contain no more than 100 gallons of milk and should contain the maximum amount of butterfat. (a) Let x be the number of gallons of milk from dairy I and let y be the number of gallons of milk from dairy II. State the objective function. Maximize z = (b) Excluding nonnegativity constraints, how many constraints are needed for this model? (b) How much milk from each dairy should the bakery use? Round your answers to the nearest integer as needed. gallons from dairy I and gallons from dairy II. (c) What is the maximum amount of butterfat? Round your answer to two decimal places as needed. gallons
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A bakery gets milk from two dairies then blends the milk to get the desired amount of butterfat for use in
the company's best selling product. Milk from dairy I costs $2.10 per gallon, and milk from dairy Il costs
$0.70 per gallon. The company has at most $140 available for purchasing milk. Dairy I can supply at most 54
gallons of milk averaging 3.8% butterfat and dairy II can supply at most 88 gallons of milk averaging 3.2%
butterfat. The blend can contain no more than 100 gallons of milk and should contain the maximum
amount of butterfat.
(a) Let x be the number of gallons of milk from dairy I and let y be the number of gallons of milk from
dairy II. State the objective function.
Maximize z=
(b) Excluding nonnegativity constraints, how many constraints are needed for this model?
(b) How much milk from each dairy should the bakery use? Round your answers to the nearest integer as
needed.
gallons from dairy I and
gallons from dairy II.
(c) What is the maximum amount of butterfat? Round your answer to two decimal places as needed.
gallons
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