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

Question

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

1/4 2/7 3/10 4/12 5/13 6/14

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, 3/10 means that if the cow is fed 3 pounds of grain supplement, the cow will produce 10 units of milk.  

How many pounds of grain supplement should Jeff feed the cows if the farm receives $0.30 per unit of milk and the price of grain supplement is $0.80 per pound?

6 pounds 5 pounds 4 pounds 2 pounds 3 pounds

Explanation / Answer

Calculate the net earnings for each scenario:

As seen from the table, the extra earnings are highest when 3 pounds of grain supplement is used.

e. 3 pounds

Extra Pounds of grain Extra units of milk Cost of grain Price of milk Extra Earnings 1 4 0.8 1.2 0.4 2 7 1.6 2.1 0.5 3 10 2.4 3 0.6 4 12 3.2 3.6 0.4 5 13 4 3.9 -0.1 6 14 4.8 4.2 -0.6

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