$5.$ Linear Programming $(6$ points$)$

Let us consider the problem faced by Foster Generators, Inc. Currently, Foster has three plants: one in Cleveland, Ohio, one in Bedford, Indiana, and one in York, Pennsylvania. Generators produced at the plants $($origins$)$ are shipped to distribution centers $($destinations$)$ in Boston, Chicago, St$.$ Louis, and Lexington, Kentucky.

Using a typical, one$-$month planning period, the production capacities at the three plants are shown in Exhibit $6\mathrm{.}10.$ Forecasts of monthly demand at the four distribution centers are shown in Exhibit $6\mathrm{.}11.$ Note that the total production capacity must be at least as large as the total demand in order to meet the forecasted demand. The transportation cost per unit for each route is shown in Exhibit $6\mathrm{.}12.$

According to above information, please help the manager to decide the best way to distribute the product from the plants to the distribution centers.