(PLEASE SOLVE USING THE TWO DIFFERENT METHODS, "LP METHOD, AND THEN SOLVE BY HEURISTIC APPROACH". SOLVE AS IF THEY WERE TWO DIFFERENT PROBLEMS, DO NOT MIX THEM SO IT IS NOT CONFUSING)

2. Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Kleins customers have already placed orders that together exceed the combined capacity of Kleins 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 the price, production costs, and transportation costs, Klein established the following profit per unit for each plantcustomer alternative:

The plant capacities and customer orders are as follows:

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.

DA Plant Clifton Springs Danville D $32 $34 Customer D, D, S34 S32 S30 S28 $40 $38 Plant Clifton Springs Capacity (units) 5000 Distributor Orders (units) D, 2000 D 5000 D, 3000 D. 2000 Danville 3000