$+$

$1.$ Suppose there are $6$ supply points, $2$ distribution centers, and $12$ demand points. The per unit cost to ship from supply point to demand point is in the matrixes below:

From$/$To

DC$1$

DC$2$

Capacity

Supplier A

$12$

$7$

$1000$

Supplier B

$13$

$9$

$800$

Supplier C

$8$

$12$

$800$

Supplier D

$6$

$9$

$1300$

Supplier E

$9$

$4$

$1200$

Supplier F

Capacity

$13$

$15$

$1000$

$6$

$7$

$6$

$8$

DC$2$

$9$

$10$

$7$

$7$

$9$

$8$

From$/$To

DP$1$

DP$2$

DP$3$

DP$4$

DP$5$

DP$6$

DP$7$

DP$8$

DP$9$

DP$10$

DP$11$

DP$12$

DC$1$

$5$

$7$

$9$

$9$

$9$

$11$

$6$

$6$

$7$

$8$

$7$

$9$

$6$

$6$

Demand

$400$

$460$

$580$

$600$

$370$

$440$

$430$

$520$

$460$

$590$

$410$

$560$

Which Suppliers should serve which DC$\text{'}$s$?$ Which DC should serve which demand points?

What is the lowest total system cost?

Adding capacity to which supplier saves us the most money?

Adding capacity to which DC saves us the most money?

How much more will it cost to serve an additional $20$ units in demand point $5?$