3. Klein Chemicals, Inc., produces a special oil-based material that is currently in short sup- ply. Four of Klein’s customers have already placed orders that together exceed the com- bined 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 dif- ferent industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying trans- portation costs between the plants and customers make a “sell to the highest bidder” strat- egy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant–customer alternative:

Plant	D 1	D 2	Customer	D 3	D 4
Clifton Springs	$32	$34		$32	$40
Danville	$34	$30		$28	$38

The plant capacities and customer orders are as follows:

Clifton Springs	5000	D 1 2000
		D 2 5000
Danville	3000	D 3 3000
		D 4 2000

How many units should each plant produce for each customer in order to maximize prof- its? Which customer demands will not be met? Show your network model and linear pro- gramming formulation.

 

View less »