A Feedlot Is Trying to Decide on the Lowest Cost

Essay

A feedlot is trying to decide on the lowest cost mix that will still provide adequate nutrition for its cattle. Suppose that the numbers in the chart represent the number of grams of ingredient per 100 grams of feed and that the cost of Feed X is $5/100 grams, Feed Y is $3/100 grams, and Feed X is $8/100 grams. Each cow will need 50 grams of A per day, 20 grams of B, 30 grams of C, and 10 grams of D. If the feedlot can get no more than 200 grams per day per cow of any of the feed types determine the constraints governing the problem.
$$\begin{array} { | l | l | l | l | } \hline \text { Ingredient } & \text { X } & \text { Y } & Z \\\hline \mathrm { A } & 10 & 15 & 5 \\\hline \mathrm { B } & 30 & 10 & 20 \\\hline \mathrm { C } & 40 & 0 & 20 \\\hline \mathrm { D } & 0 & 20 & 30 \\\hline\end{array}$$