Light$-$Twilight Inc. currently has three factories where light bulbs are manufactured, but budget cuts are forcing the company to limit production to only two of the factories. Once produced, the light bulbs are shipped to five distribution centers. The cost, demand, and maximum volume details are given as below.

Shipping cost$/1000$ bulbs $($$$)$

Warehouse

Factory

$1$

$2$

Maximum Volume $($in $1000$s$)$

Fixed Cost $($$$)$

A

$78$

$25$

$90$

$32,700$

B

$49$

$72$

$85$

$35,000$

C

$31$

$90$

$80$

$40,000$

Demand $($in $1000$s$)$

$40$

$36$

Formulate a mixed$-$integer programming model to identify which two factories the management should retain to fulfill the estimated demand while minimizing the cost. Solve the model in Excel and answer the following questions: