The Poultry Farmer Discovers, Much to His Dismay, That the Product

Essay

The poultry farmer discovers, much to his dismay, that the product mix that satisfies all of his constraints isn't really a mix of birds--it's a flock consisting of nothing but 32 Leghorns. (His constraints were a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperment less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week.) Not only is his flock going to be a very one-note mix in terms of color, he is afraid that the gleaming white feathers and deafening noise will attract predators, or worse yet, his neighbors. He immediately embarks on a breeding program to develop a Super-Cochin that can lay 4.5 eggs per week with all other performance measures the same. His optimal solution is now 27.5 Leghorns and 5.625 Super-Cochins. Assuming that he is willing to settle for a flock that has 27 Leghorns and 5 Super Cochins, what is the weekly output of eggs and performance with respect to the constraints?