Q2  Linear Programming

Suppose your company sells 4 different kinds of pies, Apple Pies, Banana Pies, Cherry Pies, and Danish Pies, where each Apple Pie sells for $8, each Banana Pie sells for $9, each Cherry Pie sells for $7, and each Danish Pie sells for $10.  Further, suppose to make these pies, each must be processed on 2 different machines in your factory and each takes a different amount of time on the two machines.  Specifically, to make one Apple Pie requires 1 hour on machine #1 and 2 hours on machine #2.  To make one Banana Pie requires 2 hours on machine #1 and 3 hours on machine #2.  To make one Cherry Pie requires 2 hours on machine #1 and 1 hour on machine #2.  And to make one Danish Pie requires 1 hour on machine #1 and 0.5 hours on machine #2.  Finally, suppose there can be no more than a total of 150 hours of processing time on machine number 1 and no more than a total of 175 hours of processing time on machine number 2.  Management has asked for your recommendation about how many of each product type to produce that maximizes revenue.

Question:

a) How much of each product do you recommend be produced that you believe maximizes revenue?  

b) How much revenue would be made if they followed your recommendation?