NEED HELP WITH B AND E$!!$

The supplies, demands, and transportation costs per unit are shown on the network. What

is the optimal $($cost$-$minimizing$)$ distribution plan?

Hart Manufacturing makes three products. Each product requires manufacturing operations

in three departments: A$,$ B$,$ and C$.$ The labour$-$hour requirements, by department, are as

follows:

During the next production period, the labor$-$hours available are $450$ in department A$,350$ in

department B$,$ and $50$ in department C$.$ The profit contributions per unit are $$25$ for product

$1,$$$28$ for product $2,$ and $$30$ for product $3.$

$($a$)$ Formulate a linear programming model for maximizing total profit contribution.

$($b$)$ Solve the linear program formulated in part $($a$).$ How much of each product should be

produced, and what is the projected total profit contribution?

$($c$)$ After evaluating the solution obtained in part $($b$),$ one of the production supervisors

noted that production setup costs had not been taken into account. She noted that

setup costs are $$400$ for product $1,$$$550$ for product $2,$ and $$600$ for product $3.$ If the

solution developed in part $($b$)$ is to be used, what is the total profit contribution after

taking into account the setup costs?

$($d$)$ Management realized that the optimal product mix, taking setup costs into account,

might be different from the one recommended in part $($b$).$ Formulate a mixed$-$integer

linear program that takes setup costs provided in part $($c$)$ into account. Management

also stated that we should not consider making more than $175$ units of product $1,150$

units of product $2,$ or $140$ units of product $3.$

$($e$)$ Solve the mixed$-$integer linear program formulated in part $($d$).$ How much of each prod$-$

uct should be produced and what is the projected total profit contribution? Compare

this profit contribution to that obtained in part $($c$).$