are $75,000$ units $at$ the Philippines plant and $100,000$ units $at$ the Mexico plant. The cost $of$ shipping from the Philippines plant $is$ $$0\mathrm{.}18$ per unit, and the cost $of$ shipping from the Mexico plant $is$ $$0\mathrm{.}10$ per unit.

Min

$s.t.$

$PT-100$ Production

$PT-200$ Production

$PT-300$ Production

Combined $PT-100$ and $PT-200$ Production Mexico Plant

Combined $PT-100$ and $PT-200$ Production Philippines Plant

$PT-300$ Production Mexico Plant

$PT-300$ Production Philippines Plant

$M_1,M_2,M_3,P_{1^{\text{'}}},P_{2^{\text{'}}},P_{3}0$

$(b)$ Solve the linear program developed $in$ part $(a)to$ determine the optimal production plan.

$(M_1,M_2,M_3,P_1,P_2,P_3)=$

What $is$ total cost $of$ the production plan $(in$ dollars$).(Round$ your answer $to$ the nearest dollar.$)$

$

$(c)$ Use $sensitivity$ analysis $to$ determine how much the production $an\frac{d}{o}r$ shipping cost per unit $(in$ dollars per unit$)$ would have $to$ change $to$ produce additional units $of$ the $PT-100in$ the Philippines plant.

$It$ would have $to$ decrease $by$ more than $ per unit.

$(d)$ Use $sensitivity$ analysis $to$ determine how much the production $an\frac{d}{o}r$ shipping cost per unit $(in$ dollars per unit$)$ would have $to$ change $to$ produce additional units $of$ the $PT-200in$ the Mexico plant.

$It$ would have $to$ decrease $by$ more than $$$ per unit.