Question: Please help! How do you calculate the cost values??? Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of
Please help! How do you calculate the cost values???



Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative: Customer Plant D1 D2 D3 D4 Clifton Springs $128 $ 136 $128 $ 160 Danville $136 $120 $112 $152 The plant capacities and customer orders are as follows: Plant Capacity (units) Distributor Orders (units) Clifton Springs 15000 D1 6000 D2 15000 Danville 9000 D39000 D46000 How many units should each plant produce for each customer in order to maximize profits? Which customer demands will not be met? Choose correct network model and Show linear programming formulation. If the constant is "1" it must be entered in the box. If your answer is zero, enter "0". Note: Dummy origin has supply of 12000. Let Xij = amount of units produced by plant node i for customer node j. 128 136 128 160 136 120 112 | Max X11 X 12 X13 X14 X21 X22 X23 152 0 0 o o + + X24 X31 X32 X33 X34 1 1 1 1 s.t. 15,000 X11 X 12 X13 X14 1 > 1 1 1 + 9,000 + X24 X21 X22 X23 1 1 1 1 12,000 Dummy + X34 X31 X32 X33 1 1 1 + X31 6,000 X11 X21 1 1 1 15,000 X12 X22 X32 1 1 1 + 9,000 X13 X23 X33 1 1 1 6,000 X14 X24 X34 Xij 2 0 for all i, j Units Cost, $ Clifton Springs - D1 o o Clifton Springs - D2 12,000 Clifton Springs - D3 o o Clifton Springs - D4 3,000 Danville - D1 6,000 Danville - D2 o o Danville D3 o o Danville - D4 3,000 Dummy - D1 o o Dummy D2 3,000 o Dummy - D3 9,000 o Dummy - D4 o o Total Cost 3,384,00 Customer 2 demand has a shortfall of 3000 Customer 3 demand of 9000 is not satisfied