Blending The Mostpure Milk Company gets milk from two dairies and then blends the milk to get the desired amount of butterfat for the company's premier product. Milk from dairy I costs $2.40 per gal, and milk from dairy II costs $0.80 per gal. At most $144 is available for purchasing milk. Dairy I can supply at most 50 gal of milk averaging 3.7% butterfat. Dairy II can supply at most 80 gal of milk, averaging 3.2% butterfat.
(a) How much milk from each dairy should Mostpure use to get at most 100 gal of milk with the maximum total amount of butterfat? What is the maximum amount of butterfat?
(b) The solution from part (a) leaves both dairy I and dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce. Is there any way all this capacity could be used while still meeting the other constraints? Explain.
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