Question

A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy costs $2.40 per gallon, and milk from dairy II costs $0.80 per gallon. At most $144 is available for purchasing milk. Dairy I can supply at most 50 gallons averaging 3.9% butterfat, and dairy Il can supply at most 90 gallons averaging 2.9% butterfat. Answer parts a and b. a How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of butterfat? The company should buy gallons from dairyl and gallons from dairy II.

Answer 1

Answer 1: Let the amount of milk bought from Dairy 1 be x gallons

Amount bought from Dairy 2 will be ( 100 - x ) gallons

Cost = 2.40x + ( 100 - x ) 0.80 = $144.00

2.4x + 80 - 0.80x = $144

1.6x = 64

x = 64 / 1.6 = 40 gallons

Dairy 1 = 40 gallons

Dairy 2 = 60 gallons

The company should buy 40 gallons from Dairy 1 and 60 gallons from Dairy 2.

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