Q$2.$

The U$.$S$.$ Cable Company uses a distribution system with five distribution centers and eight customer zones. Each customer zone is assigned a sole source supplier, each customer 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 customer zones. The following table shows the five distribution centers and cost of supplying each customer zone $($in thousands of dollars$)$:

Customer Zones

Distribution Centers

Los Angeles

Kansas City

Chicago

Columbus

Atlanta

Newark

Denver

Dallas

I

Plano

$70$

$47$

$22$

$53$

$98$

$21$

$27$

$13$

Nashville

Flagstaff

Springfield

Boulder

$75$

$19$

$58$

$90$

$34$

$40$

$26$

$15$

$7830$

$37$

$82$

$40$

$29$

$32$

$60$

$45$

$8$

$39$

$82$

$36$

$32$

$45$

$29$

$75$

$86$

$25$

$11$

$37$

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

cost$.$