A small company builds three products, A, B, and C, which earn profits of $150, $200, and $300, respectively. Each product requires machine time and raw material; there are 600 hours of machine time and 750 pounds of raw material available. Each unit of product A requires 3 hours of machine time and 2 pounds of raw material, each unit of product B requires 4 hours of machine time and 4 pounds of raw material, and each unit of product C requires 5 hours of machine time and 8 pounds of raw material. How many of each product should be built in order to maximize profit?

a) Set up LP Model. Either write it down or include your Excel work below.

b) What is the optimal combination of products and what is the best profit?

 

c) How much is an extra hour of machine time be worth? How much is an extra pound of raw material worth? Fractional answers are OK here. (Hint: This is called the shadow price.) d) How does the solution change if we must produce at least 20 units of each product and ensure that the answers are integers? What is the new optimal combination of products and the new optimal profit?