Consider the following network representation of a transportation problem. The supplies, demands, and transportation costs per unit are shown on the network. (a) Develop a linear programming model for this problem; be sure to define the variables in your model. Let x11= amount shipped from Jefferson City to Des Moines x12= amount shipped from Jefferson City to Kansas City x13= amount shipped from Jefferson City to St. Louis x21= amount shipped from Omaha to Des Moines x22= amount shipped from Omaha to Kansas City x23= amount shipped from Omaha to St. Louis Minx11+x12+x13+x21+x22+x23s.t.x11+x12+x13x11+x21=x12+x22=x13+x23=x11,x12,x13,x21,x22,x230 (b) Solve the linear program to determine the optimal solution