The owner of a small chicken farm must determine a laying and hatching program for 100 hens. There are currently 100 eggs in the henhouse and the hens can be used either to hatch existing eggs or to lay new ones. In each 10-day period, a hen can either hatch 4 eggs or lay 12 new ones. Chicks that are hatched can be sold for $1.10 each, and every 30 days an eggs dealer gives 18 cents each for the eggs accumulated to date. Eggs not being hatched in one period can be kept in a special incubator room for hatching in a later period. The problem is to determine how many hens should be hatching and how many should be laying in each of the next three 10-day periods so that the total revenue is maximized. Formulate a linear program to solve this problem. (Define all the decision variables precisely.)