The manger of O'Brian glass company is planning the production of automobile windshields for the next four months. The demand for the next four months is projected to be as shown in the following table
month demand for windshields
1 130
2 140
3 260
4 120
O'Brian can normally produce 100 windshields in a month. This is done during regular production hours at a cost of 100 dollars per windshield. If demand in any one month cannot be satisfied by regular production, the production manager has three other choices: (1) he can produce up to 50 more windshields per month in overtime but at a cost of 130 dollars per windshield; (20) he can produce a limited number of windshields from a friendly competitor for resale at a cost of 150 dollars each (the maximum number of outside purchase over the four-month period is 450 windshields); or (3) he can fill the demand from his on-hand inventory. The inventory carrying cost is 10 dollars per windshield per month. Back orders are not permitted. Inventory on hand at the beginning of month 1 is 40 windshields,. Set up and solve this "production smoothing" problem as a transportation model to minimize cost. Hint set the various production options as supply nodes and the monthly demands as the demand nodes.