Steel mills in three cities produce the following amounts of steel:

Location Weekly Production (tons)

A. Bethlehem 150 B. Birmingham 210 C. Gary 320 680 These mills supply steel to four cities, where manufacturing plants have the following demand:

Location Weekly Demand (tons) 1. Detroit 130 2. St. Louis 70 3. Chicago 180 4.

Norfolk 240 620 Shipping costs per ton of steel are as follows:
To (cost)
From 1 2 3 4 A $14 $ 9 $16 $18 B 11 8 7 16 C 16 12 10 22 Because of a truckers’ strike, shipments are prohibited from Birmingham to Chicago.

a. Formulate this problem as a linear programming model, and solve it using the computer.

b. What would be the effect on the optimal solution of a reduction in production capacity at the Gary mill from 320 tons to 290 tons per week?