The Alpha Beta Corporation Makes Laser and Ink Jet Printers

Essay

The Alpha Beta Corporation makes laser and ink jet printers for personal computers. Each laser printer yields $40.00 in profits and each ink jet printer provides $20.00. Each of the printers goes through two assembly areas. The following table provides processing times per unit in minutes) as well as total available processing times per department:
$$\begin{array} { l c c } \underline{\text { Printer} } & \underline{ \text { Dept. A }} & \underline{\text { Dept. B }} \\\text { Laser }& 9 & 12 \\\text { Ink jet } & 6 & 8 \\\text { Tatal time per day } & 216 & 384\end{array}$$
Sales commitments require at least 5 laser printers and 10 ink jet printers to be made per day. The company is interested in determining how many of each printer to produce so as to maximize its profit.
a. What is the objective function for this LP problem?
b. What are the constraints corresponding to Dept. A if X1 corresponds to laser printers?
c. What are the optimum solution points for this problem?
d. What is the optimal value of the objective function?