Klein Chemicals, Inc., produces a special oil-base material that is currently in short suply. For 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 all 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 $32 $34 $32 $40
Danville $34 $30 $28 $38
The plant capacities and customer orders are as follows:
Plant Capacity (units) Distributor Order (units)
Clifton Springs 5000 D1 2000
D2 5000
Danville 3000 D3 3000
D4 2000
How many units should each plant produce for each customer to maximize profits?
Which customer demands will not be met?
Show your network model and linear programming formulation.