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, Dallas, and Jasper counties. Two trucks have 15-ton capacities, and the third truck has a 30-ton capac- ity. 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 P = amount shipped to Polk County D = amount shipped to Dallas County J = amount shipped to Jasper County 1 if the 30-ton truck is assigned to county i Yi = e 0 otherwise
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 mixedinteger linear program to determine how much to ship to each county.