Spring Is Right Around the Corner and That Can Mean

Essay

Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs.


$$\begin{array} { | l | c | c | c | } \hline \text { Bird } & \text { Leghorn } & \text { Cochin } & \text { Buff Orpington } \\\hline \text { Eggs/week } & 5 & 2 & 4.5 \\\hline \text { Plumage } & 3 & 9 & 6 \\\hline \text { Temperment } & 2 & 8 & 5 \\\hline \text { Fertilizer } & 3 & 2 & 4 \\\hline \text { Appetite } & 5 & 4 & 8 \\\hline\end{array}$$
Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week.
-What is a full set of constraints if the farmer wants this flock to produce less than 100 decibels of noise and more than 5 pounds of fertilizer, consume less than 10 pounds of layer pellets, and achieve a total plumage score of at least 75?