A dairy company gets milk from two dairies and then blends the milk to get the d

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 cost $2.40 per gallon, and milk from dairy II cost $0.80 per gallon. At most $144 is availible for purchasing milk. Dairy I can supply almost 55 gallons averaging 3.9% butterfat, and dairy II can supply at most 80 gallons averaging 2.9% buttefat. answer part a and b A. how much milk from each supplier should the cocmpany 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 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. The excess of dairy I is ___ gallons, and for dairy II is it ___ gallons.

Explanation / Answer

Cost of Milk from Dairy1 with fat 3.9% & Maximum supply of 55 Gallons= $2.40/gallon;

Cost of Milk from Dairy2 with fat 2.9% & Maximum supply of 80 Gallons= $0.80/gallon;  

Maximum money available for purchasing milk = $144

Let the quantity purchased from Dairy1 = X gallon & Let the quantity purchased from Dairy2 = Y gallon

To buy milk with maximum amount of butterfat i.e. 3.9% at most by 100 gallons i.e. =< 100 will be 55 Gallons from Dairy1 at $132.

Ans is A. 55 gallons from Dairy1 & 0 gallons from Dairy2 B. Excess of Dairy1 is 0 gallons & Dairy2 is 80 gallons

But to buy 100 gallons of milk with maximum fat

X + Y = 100 & 2.4X + 0.8Y = 144 => X = 40 & Y = 60

Ans is A. 40 gallons from Dairy1 & 60 gallons from Dairy2 with butterfat 3.3% B. Excess of Dairy1 is 15 gallons & Dairy2 is 20 gallons

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