An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 3

Yates Company supplies road salt to county highway departments. The company has three trucks, and the dispatcher is trying to schedule tomorrow's deliveries to polk, Daltas, and Jasper counties. Two trucks have 15-ton capacities, and the third truck has a 30-ton capacity. Based on these truck capacities, two counties will receive 15 tons and the third will
Receive 30 tons of road salt. The dispatcher wants to determine how much to ship to each county. Let
and
a. Use these variable definitions and write constraints that appropriately restrict the amount shipped to each county.
b. The cost of assigning the 30-ton truck to the three counties is $100 to Polk, $85 to Dallas, and $50 to Jasper. Formulate and solve a mixed-integer linear program to determine how much to ship to each county.