USE LINGO TO SOLVE

$1.$ a$.$ Formulate and solve the base model. Report the results and explain one reduced cost and one shadow price as applicable to the problem.

b$.$ Remodel the problem #$1($ optimal feed mix$)$ with the following constraints: $-$ Include a budgetary restriction of $$750.-$ Demand for both feed$1$ and feed $2$ are restricted to $1000$lbs each. Compare and comment on the results with the optimal solution of the base model.

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 $50\frac{c}{l}b$ and

up to $800lb$ of alfalfa at $40\frac{d}{l}b.$ Demand for each type of

feed is unlimited. Formulate an LP to maximize Feedco's

profit.