A manager wants to know how many units of each product to produce on a daily basis in order to achieve the highest contribution to profit. Production resource and material requirements for the products are shown in the following table. Material 1 costs $8.50 a pound, material 2 costs $6.25 a pound, and labor costs $12 an hour. Management considers equipment hours as overhead and chooses to not include it in product costing (the wisdom of that decision is up for debate). Product A sells for $90 a unit, product B sells for $100 a unit, and product C sells for $78 a unit. Available resources each day are 1200 pounds of material 1, 1,400 pounds of material 2, 1,000 hours of labor and 700 hours equipment time. The manager must satisfy certain output requirements: - The output of product A should be at least of the total number of units produced - There is a standing order for 50 units of product B each day. - We can sell no more than 75 units of product C each day. a. Formulate an LP model for this problem (i.e. the standard table format from PowerPoint and in class.) Define your decision variables, create the objective function formula in terms of your decision variables, and create and label your constraints. Just type this into Sheet 1 of your Excel file in a text box or use Equation Editor. (3 points) e.g. something like: Decision Variables: x1 = the number of product X to make x2 = the number of product Y to make and so on . . . . Constraints: max 2 x1 + 3 x2 + x3 + 4x4 subject to: x1 + 3 x2 + 5 x3 + x4

\begin{tabular}{|c|c|c|c|c|} \hline Product & \begin{tabular}{c} Material 1 \\ (pounds) \end{tabular} & \begin{tabular}{c} Material 2 \\ (pounds) \end{tabular} & \begin{tabular}{c} Labor \\ (hours) \end{tabular} & \begin{tabular}{c} Equipment \\ (hours) \end{tabular} \\ \hline A & 2.5 & 3 & 2.5 & 2 \\ \hline B & 3 & 5 & 1.4 & 1.6 \\ \hline C & 4 & 0 & 1.75 & 1.5 \\ \hline \end{tabular}