The U$.$S$.$ Cable Company uses a distribution system with five distribution centers and

Los

Angeles

$21.$

eight customer zones. Each customer zone is assigned a sole source supplier; each cus$-$

tomer zone receives all of its cable products from the same distribution center. In an effort

to balance demand and workload at the distribution centers, the company$$s vice president

of logistics specified that distribution centers may not be assigned more than three cus$-$

tomer zones. The following table shows the five distribution centers and cost of supplying

each customer zone $($in thousands of dollars$)$:

Customer Zones

: $$ Kansas

Chicago Columbus Atlanta Newark City Denver $\_$ Dallas

$4722$ oe $98$ ZL $2,13$

$38195890344026$

$78$ oy $82111402932$

$2383982368245$

$40297586251137$

a$.$ Determine the assignment of customer zones to distribution centers that will minimize

cost$.$

b$.$ Which distribution centers, if any, are not used?

c$.$ Suppose that each distribution center is limited to a maximum of two customer zones.

How does this constraint change the assignment and the cost of supplying customer

zones