$($a$)$ Why is the company considering opening at least one new plant?

$($b$)$ How many shipment variables will the LP formulation have? $($That is$,$ how many Xij variables are

included in the formulation?$)$

$($c$)$ Why do we need to introduce binary variables YC$,$ YD$,$ YE and YF$?$ Do we need a binary

variables YA and YB$?$ Why?

$($d$)$ Formulate a linear programming model for minimizing total costs $($shipping costs$+$fixed costs$)$;

you should have a total of $9$ constraints. You can use steps $($i$)-($iv$)$ below as a guide for writing the LP

i$.$ Use suitable variables to express the objective function $($minimize shipping costs $+$ fixed costs$).$

ii$.$ Write the demand constraints for Distribution Centers $1,2$ and $3.$

iii. Write the supply constraints for plants A and B$.$

iv$.$ Use suitable variables to write the supply constraints for plants C$,$ D$,$ E and F$.$

$($e$)$ Write a constraint to express a requirement that the company will open only one new plant

$($f$)$ If the company will open only one plant, which plant do you think it will be C$,$ D$,$ E or F$?$ Why?

$($g$)$ Write a constraint to express a requirement that the company will either open both plants C and

D or neither of them $($that is$,$ if plant C opens then plant D has to open as well and if plant D is

open then Plant C has to open too$)$

Extra credit option I $(4$ points$)$:

Use Excel solver to solve the linear program formulated in part $($d$)$: Which plants will open and what is the

shipping plan $($i$.$e$.,$ how many units will be shipped from each plant to each distribution center?$)$

What is the associated costs of this plan?

Extra credit option II $(2$ points$)$:

Use Excel solver to solve the linear program formulated in part $($d$)$ with the additional constraint you

determined in $($e$).$ Which plant will open and how many units will be shipped from each plant to each

distribution center? What is the associated costs of this plan?