Mr. McGregor owns a 5-acre cabbage patch. He forces his wife, Flopsy, and his son, Peter, to work in the cabbage patch without wages. Assume for the time being that the land can be used for nothing other than cabbages and that Flopsy and Peter can find no alternative employment. The only input that Mr. McGregor pays for is fertilizer. If he uses x sacks of fertilizer, the amount of cabbages that he gets is 10 √ x. Fertilizer costs $1 per sack.
(a) What is the total cost of the fertilizer needed to produce 100 cabbages? ______. What is the total cost of the amount of fertilizer needed to produce y cabbages? _____.
(b) If the only way that Mr. McGregor can vary his output is by varying the amount of fertilizer applied to his cabbage patch, write an expression for his marginal cost, as a function of y. MC(y) = ______.
(c) If the price of cabbages is $2 each, how many cabbages will Mr. Mc-Gregor produce? _____. How many sacks of fertilizer will he buy? _____. How much profit will he make? ______.
(d) The price of fertilizer and of cabbages remain as before, but Mr. Mc-Gregor learns that he could find summer jobs for Flopsy and Peter in a local sweatshop. Flopsy and Peter would together earn $300 for the summer, which Mr. McGregor could pocket, but they would have no time to work in the cabbage patch. Without their labor, he would get no cabbages. Now what is Mr. McGregor’s total cost of producing y cabbages? ______________.
(e) Should he continue to grow cabbages or should he put Flopsy and Peter to work in the sweatshop?