Final answer:
In a typical transportation problem with four sources and three destinations, there will be 12 decision variables.
Step-by-step explanation:
A typical transportation problem with four sources and three destinations will have 4 x 3 = 12 decision variables. Each variable represents the quantity to be shipped from each source to each destination.
For example, if the sources are labeled A, B, C, and D, and the destinations are 1, 2, and 3, the decision variables will be xA1, xA2, xA3, xB1, xB2, xB3, xC1, xC2, xC3, xD1, xD2, and xD3, where xA1 is the amount transported from source A to destination 1, and so on.
The goal of the linear program is often to minimize the cost of transportation while satisfying supply and demand constraints at the sources and the destinations, respectively.