$($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 $($in

dollars$)?$

$(P_1,P_2,P_3)=(,)$ with profit $$,.$

$($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 $$410$ for product $1,$$$600$ for product $2,$ and $$570$ for product $3.$ If the solution developed in part $($b$)$ is to be used, what is the

total profit contribution $($in dollars$)$ 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 into account. Management also stated that we should not consider making more than $160$ units of

product $1,175$ units of product $2,$ or $185$ units of product $3.($Let $P_i=$ units of product i produced and $y_i$ be the $0-1$ variable that is one if any quantity of

product $i$ is produced and zero otherwise, for $i=1,2,3.)$

What is the objective function of the mixed$-$integer linear program?

Max $160P_1+175P_2+185P_3-410Y_1-600Y_2-570Y_3$

Capitalization of variable$($s$)$ is important. Check that your upper and lower case match the question.

In addition to the constraints from part $($a$),$ what other constraints should be added to the mixed$-$integer linear program?

s$.$t$.$

units of Product $1$ produced

units of Product $2$ produced

units of Product $3$ produced

$P_1,P_2,P_{3}0$;$y_1,y_2,y_3=0,1$

$($e$)$ Solve the mixed$-$integer linear program formulated in part $($d$).$ How much of each product should be produced, and what is the projected total profit $($in

dollars$)$ contribution?