Let P$1=$ number of PT$-100$ battery packs produced at the Philippines plant $($b$)$ Solve the linear program developed in part $($a$),$ to determine the optimal production plan. If the amount is zero, enter $"0".$

Total Cost $=$ s

$($c$)$ Use sensitivity analysis to determine how much the production and$/$or shipping cost per unit would have to change to produce additional units of the PT$-100$ in the Philippines plant.

If required, round your answer to two decimal digits.

At least $$\frac{,}{?}$ unit.

$($d$)$ Use sensitivity analysis to determine how much the production and$/$or shipping cost per unit would have to change to produce additional units of the PT$-200$ in the Mexico plant.

If required, round your answer to two decimal digits.

At least $

$/$ unit.

$P2=$ number of PT$-200$ battery packs produced at the Philippines plant

P$3=$ number of PT$-300$ battery packs produced at the Philippines plant

M$1=$ number of PT$-100$ battery packs produced at the Mexico plant

M$2=$ number of PT$-200$ battery packs produced at the Mexico plant

M$3=$ number of PT$-300$ battery packs produced at the Mexico plant

$\frac{?}{\text{b}\text{a}\text{r}}(p_1+)$

$\frac{?}{\text{b}\text{a}\text{r}}{(}_2+)$

$\frac{?}{\text{b}\text{a}\text{r}}(P3+)$

$\frac{?}{\text{b}\text{a}\text{r}}(u_1+)$

$\frac{?}{\text{b}\text{a}\text{r}}(42+)$

M$3$

s$.$t$.$

$P1+$

$P2+$

$P3+$

$M1+M2+$

$M3=$

Production PT$-100$

$P1+$

$P2+$

P$3+$

$M1+$

$M2+$

$M3=$

Production PT$-200$

$P1+$

$P2+$

$P3+$

$M1+$

$M2+$

$M3=$

Production PT$-300$

$r_1+2+$

$P3+$

$M1+$

$M2+$

$13$

Production PT$-300$ Capacity Phi PT$-100$ & $200$

$M2+$

$M1+$

$13$

Capacity Mex PT$-100$ & $200$

$P1+$

${?}_2+$

$P_3+$

$M1+$

$M2+$

$13$

Capacity Phi PT$-300$

P$1+$

$P2+$

$P3+$

$M1+$

$M2+$

M$3$

Capacity Mex PT$-300$

$P1,P2,P3,M1,M2,M30$

$P2+$

$P3+$

$\begin{array}{cc}M1+M2+& M3\end{array}$ Capacity Mex $PT-300$