Question

A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I 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 3.7% butterfat, and dairy II 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 dairy I and __ gallons from dairy II.

Answer 1

Let the company should buy x gallons milk from dairy I and y gallons milk from dairy II and total supply of butterfat be z gallons.

Then the problem becomes,

Maximize z = (x*3.7%)+(y*2.9%)

Subject to x+y 100

x 50

y 90

2.4x+0.8y 144

x, y 0

i.e., Maximize z = 0.037x+0.029y

Subject to x+y 100

x 50

y 90

2.4x+0.8y 144

x, y 0

Now we solve this problem using Excel.

Therefore, the company should buy 40 gallons milk from dairy I and 60 gallons milk from dairy II.

We were unable to transcribe this image