A manufacturer produces a product at three plants and distributes the product through four market-service warehouses. The following tables provide data pertinent to the production and distribution for the firm. Table 1 provides the price the warehouses charge their retail customers and the demand (units that can be sold) at each warehouse. Table 2 provides the cost of producing each unit at each plant and the capacity at each plant. Table 3 provides the transportation cost of shipping each unit between the plants and the warehouses.

Table 1: Warehouse Price and Demand

Warehouse	Selling Price per Unit	Annual Demand (units)
Warehouse 1	$1.00	40,000
Warehouse 2	$1.10	10,000
Warehouse 3	$1.00	20,000
Warehouse 4	$0.60	25,000

Table 2: Plant Costs and Capacity

Plant	Unit Variable Production Cost	Annual Capacity
Plant A	$0.40	40,000
Plant B	$0.35	30,000
Plant C	$0.45	45,000

Table 3: Transportation Cost from Plant to Warehouse

	Warehouse 1	Warehouse 2	Warehouse 3	Warehouse 4
Plant A	$0.20	$0.20	$0.30	$0.30
Plant B	$0.20	$0.10	$0.35	$0.40
Plant C	$0.45	$0.30	$0.20	$0.20

1. Suppose the production manager wants to meet all demand at the minimum cost. Formulate a linear program that will provide the optimal production and distribution schedule.
2. Suppose the group vice president wishes to meet only the demands that will maximize profits. Modify your LP formulation to provide the production and distribution schedule that maximizes profits.

Hint: For #1, you may want to combine the variable production cost with the transportation costs to get one matrix for the unit cost on each distribution route. In part 2, you are maximizing total profit. You can do this by using a per unit profit matrix by subtracting the per unit costs from the selling price per unit.