The Happy Pet Pet Food Company Produces Dog and Cat

Essay

The Happy Pet pet food company produces dog and cat food. Each food is comprised of meat, soybeans and fillers. The company earns a profit on each product but there is a limited demand for them. The pounds of ingredients required and available, profits and demand are summarized in the following table. The company wants to plan their product mix, in terms of the number of bags produced, in order to maximize profit.
$$\begin{array} { l c c c c c } \text { Product } & \begin{array} { c } \text { Profit per } \\\text { Bag } ( \$ )\end{array} & \begin{array} { c } \text { Demand for } \\\text { product }\end{array} & \begin{array} { c } \text { Pounds of } \\\text { Meat per bag }\end{array} & \begin{array} { c } \text { Pounds of Soybeans } \\\text { per bag }\end{array} & \begin{array} { c } \text { Pounds of } \\\text { Filler per bag }\end{array} \\\hline \text { Dog food } & 4 & 40 & 4 & 6 & 4 \\\text { Cat food } & 5 & 30 & 5 & 3 & 10 \\\hline && \text { Material available (pounds) } & 100 & 120 & 160\end{array}$$
a.
Formulate the LP model for this problem.
b.
Solve the problem using the graphical method.