Problem 8 (Adapted from Winston, 2004): Feedco produces two types of cattle feed, both consisting totally of wheat and alfalfa. Feed 1 must contain at least 75% wheat, and feed 2 must contain at least 60% alfalfa. Feed 1 sells for $2.00/lb and feed 2 sells for $1.75/lb. Feedco can purchase up to 1,000 lb of wheat at $0.60/1b and up to 750 lb of alfalfa at $0.45/lb. Demand for each type of feed is unlimited. Parta: Formulate an LP to maximize Feedco's profit. Part b: Feedco has decided to give its customer (assume it has only one customer) a quantity discount. If the customer purchases more than 300 lb of feed 1, each pound over the first 300 lb will sell for only $1.65/b. Similarly, if the customer purchases more than 300 pounds of feed 2, each pound over the first 300 lb will sell for $1.50/1b. Modify the LP from part a to account for the presence of quantity discounts. (Hint: There are a couple ways to do this. You could use soft constraints, or you could define variables to represent the feed sold at each price.)