Jack knows that adding a special grain supplement to his cows will produce more

Question

Jack knows that adding a special grain supplement to his cows will produce more milk according to the following schedule:

1/3 2/5 3/7 4/8 5/8.65 6/8.75;  

where the first number reports the total number of pounds of grain supplement, and the second number reports the total amount of milk produced. For example, 3/7 means that if the cow is fed 3 pounds of grain supplement, the cow will produce 7 units of milk.  

How many pounds of grain supplement should Jack feed the cows if the farm receives $0.50 per unit of milk and the price of grain supplement is $0.30 per pound?

5 pounds 4 pounds 2 pounds 6 pounds 3 pounds

Explanation / Answer

Calculate the net earnings for each scenario:

The net earnings are highest when 5 pounds of grain supplement is used.

a. 5 pounds

Extra Pounds of grain Extra units of milk Cost of grain Price of milk Net Earnings 1 3 0.3 1.5 1.2 2 5 0.6 2.5 1.9 3 7 0.9 3.5 2.6 4 8 1.2 4 2.8 5 8.65 1.5 4.325 2.825 6 8.75 1.8 4.375 2.575

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