1) (7 points) A small company builds two products, X and Y, which earn profits of $24 and $17, respectively. Each product requires machine time and raw material; there are 4000 hours of machine time and 6000 pounds of raw material available. Each unit of product X requires 3 hours of machine time and 6 pounds of raw material; each unit of product Y requires 4 hours of machine time and 3 pounds of raw material. Lastly, due to a pre-existing order, we must produce at least 460 units of product Y. 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 best profit?

c) How much money would 30 extra hours of machine time be worth? How much money would 30 extra pounds of raw material worth? (This is called the shadow price.)

d) How does the solution change if we must balance production for X and Y that is, make the same amount of both and ensure that the answers are integers? What are the new optimal combination of products and best profit?