Suppose a profit maximizing company in West Virginia contracts with poultry (chickens) farmers in three regions which produce up to 4,000, 5,000, and 6,000 lbs/week. There are two processing plants. Three resources are required to operate each processing plant: labor, capital goods (machinery, buildings, etc.) and chickens. Labor is paid $1.25/hour and capital resources are paid $0.4/capital hour. One of the plants is newer and is less labor intensive and more capital intensive than the other. The quantities of three resources needed to make one case of frozen chickens at each processing plant are:

                          Plant1    Plant2

Labor (hours)       0.04      0.08

Capital (hours)     2.00       1.45

Chickens (lbs)      16.0      16.0

The unit transportation costs for shipping the freshly harvested chickens from the growing regions to the processing plants are

                              Plant1($/lbs)   Plant2($/lbs)

Region1                        0.02      0.04

Region2                          0.01      0.03

Region3                           0.04     0.01

If the price of a case of frozen chickens is $12.5, what is the best way to process the chickens each week and what is your total revenue?

1. Show a mathematical representation of this problem