Reconsider the pig problem of Example $1\mathrm{.}1,$ but now assume that the price

for pigs is starting to level off. Let

$p=0\mathrm{.}65-0\mathrm{.}01t+0\mathrm{.}00004t^2$

represent the price for pigs $($cents$/$lb$)$ after $t$ days.

$($a$)$ Use MATLAB to graph eqn. $(1)$ along with our original price equation.

$($b$)$ Find the best time to sell the pig.

$($c$)$ The parameter $0\mathrm{.}00004$ represents the rate at which price is leveling off.

Conduct a sensitivity analysis on this parameter. Consider both the optimal

time to sell and the resulting profit.

$($d$)$ Compare the results of part $($b$)$ to the optimal solution contained in the

text. Comment on the robustness of our assumptions about price.