(b) Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs. Let x11= amount shipped from Southern Gas to Hamilton x12= amount shipped from Southern Gas to Butler x13= amount shipped from Southern Gas to Clermont x21= amount shipped from Northwest Gas to Hamilton x22= amount shipped from Northwest Gas to Butler x23= amount shipped from Northwest Gas to Clermont x11+x12+x13x12+x22=200x13+x23= (c) Describe the distribution plan and show the total distribution cost. (ii) Create an updated distribution plan assuming Northwest Gas becomes the preferred supplier. housands of dollars) are as follows