Problem $3(15$ points$).$ Feedco produces two types of cattle feed, both consisting totally of wheat and alfalfa.

Feed $1$ must contain at least $80\%$ wheat, and feed $2$ must contain at least $60\%$ alfalfa. Feed $1$ sells for

$$\frac{1\mathrm{.}50}{l}b,$ and feed $2$ sells for $$\frac{1\mathrm{.}30}{l}b.$ Feedco can purchase up to $1,000lb$ of wheat at $$\frac{0\mathrm{.}50}{l}b$ and up

to $800$ lb of alfalfa at $$\frac{0\mathrm{.}40}{l}b.$ Demand for each type of feed is unlimited. Formulate an LP to maximize

Feedco's profit.

Problem $8(1\mathrm{.}5$ bonus points$).$ Feedco $($see Problem $3)$ 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 $$\frac{1\mathrm{.}25}{l}b.$ Similarly, if the customer purchases more than $300$ pounds of feed

$2,$ each pound over the first $300$ lb will sell for $$\frac{1\mathrm{.}00}{l}b.$ Modify the LP of Problem $3$ to account for the

presence of quantity discounts. $($Hint: Define variables for the feed sold at each price.$)$