Answer Happy

A large textile firm has two manufacturing plants (A,B), two sources (S1,S2) of raw material, and three market centers (M1, M2, M3). The transportation costs between the sources and the plants and between the plants and the markets are as follows: Source Plant A Plant B Si 1 $/ton 1.50 $/ton S2 2 $/ton 1.50 $/ton Plant A B Mi M2 M3 4 $/ton 2 $/ton 1 $/ton 3 $/ton 4 $/ton 2 $/ton Ten tons are available from S1 and 15 tons from S2. The three market centers require 8, 14 and 3 tons, respectively. The plants have unlimited processing capacity. • Formulate and solve the optimization problem for finding the shipping pat- terns from sources to plants to markets that minimizes the total transporta- tion cost. • Solve again the above optimization problems but this time assume that plant A has a processing capacity of 8 tons, whereas plant B has a processing capacity of 7 tons.