$75,000$ units at the Philippines plant and $100,000$ units at the Mexico plant. The cost of shipping from the Philippines plant is $$0\mathrm{.}21$ per unit, and the cost of shipping from the Mexico plant is $$0\mathrm{.}08$ per unit.

Let P$1=$ number of PT$-100$ battery packs produced at the Philippines plant

P$2=$ 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

$($b$)$ Solve the linear program developed in part $($a$)$ to determine the optimal production plan. If the amount is zero, enter $"0".$

Total Cost $=$ :

$($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

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

$\text{'}$ unit.