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 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 80 gallons averaging 2.9% butterfat. Answer parts a and b. 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. What is the maximum amount of butterfat? Gallons (Type an integer or a decimal.) 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 capacity of dairy I is gallons, and for dairy II it is gallons. Is there any way all this capacity could be used while still meeting the other constraints? Explain. Yes, 10 more gallons can be bought from dairy I without going over budget. Yes, 10 more gallons can be bought from dairy I without going over budget. Yes, 10 more gallons can be bought from dairy I and 20 more from dairy II without going over budget. No. Any more milk purchased from either dairy will go over budget.

Explanation / Answer

2.4X+0.8Y<=144

or 3x+y<= 180

(60,0) (0,180) can be done

But max of X is 50 and max of y is 80

Hence either (50, 30) Or (33,80) can be chosen

Z for (50,30) = 3.7(50)+2.9(30)=272

Z for (33,80) = 3.7(33)+2.9(80)=354.10

Hence maximum fat at 354.10 when (x,y) = (33,80)

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Excess capacity is 17 galons for X(Dairy I)

Option D

Dairy I II cost/galon 2.4 0.8 2.4x+0.8y Supply(galons) 50 80 Butterfat 3.70% 2.90% Maximise z 3.7x+2.9Y

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