Question
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
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. Kleins 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 plantcustomer alternative:
| Customer | ||||||||
| Plant | D1 | D2 | D3 | D4 | ||||
| Clifton Springs | $96 | $102 | $96 | $120 | ||||
| Danville | $102 | $90 | $84 | $114 | ||||
The plant capacities and customer orders are as follows:
| Plant | Capacity (units) | Distributor Orders (units) | |||
| Clifton Springs | 25000 | D1 10000 | |||
| D2 25000 | |||||
| Danville | 15000 | D315000 | |||
| D410000 | |||||
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 20000.
which model is correct?
Let xij = amount of units produced by plant node i for customer node j.
| Max | x11 | + | x12 | + | x13 | + | x14 | + | x21 | + | x22 | + | x23 | |||||
| + | x24 | + | x31 | + | x32 | + | x33 | + | x34 | |||||||||
| s.t. | x11 | + | x12 | + | x13 | + | x14 | |||||||||||
| x21 | + | x22 | + | x23 | + | x24 | ||||||||||||
| x31 | + | x32 | + | x33 | + | x34 | Dummy | |||||||||||
| x11 | + | x21 | + | x31 | = | |||||||||||||
| x12 | + | x22 | + | x32 | = | |||||||||||||
| x13 | + | x23 | + | x33 | = | |||||||||||||
| x14 | + | x24 | + | x34 | = | |||||||||||||
| xij 0 for all i, j | ||||||||||||||||||
| Units | Cost, $ | |
| Clifton Springs - D1 | ||
| Clifton Springs - D2 | ||
| Clifton Springs - D3 | ||
| Clifton Springs - D4 | ||
| Danville - D1 | ||
| Danville - D2 | ||
| Danville - D3 | ||
| Danville - D4 | ||
| Dummy - D1 | ||
| Dummy - D2 | ||
| Dummy - D3 | ||
| Dummy - D4 | ||
| Total Cost |
demand has a shortfall of .
demand of is not satisfied.
1 5000s 25000D 15000 D Duy 2000 10000 D 4 D2 5000 DS 15000 20000 0000DStep by Step Solution
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