Problem 1 (0.4 points): Linear programming can be used to optimize the cost of goods transportation between different selling points. The following is a simplified version of such an approach. Solodrex manufacutres a brand of cheese in 2 factories and sells its production through 5 sales outlets in California. The demands of the market have changed in different areas this month and therefore, this weekend Solodrex intends to produce and redistibute cheese stocks to its 5 sales outlets. Current stocks and the needed stocks at each outlet are given in the table below. Current Stock (1b) Needed Stock (1b) Outlet 1 1,250 2,500 Outlet 2 1,700 1,000 Outlet 3 1,400 1,800 Outlet 4 1,200 3,000 Outlet 5 1,000 2,000 The two factories of Solodrex (Factory 1 and Factory 2) can manufacture cheese at a cost of pi and p2 $ per lb, respectively. The manufactured stock as well as the stock available at each outlet can be moved through the roads connecting them which are shown in the figure. The cost per lb of transportation through these roads (in either direction) is also shown. C13 Outlet 3 Outlet 1 C34 Cfil C12 C23 Outlet 4 Outlet 2 Factory 1 Cf24 C25 Cf15 Cf25 Outlet 5 Factory 2 Write an LP that will enable Solodrex to minimize the cost needed to meet the new market re- quirement