Question

WestFuel produces a special fuel system component at its three plants. The company currently has orders from four customers. After considering relevant costs, WestFuel can expect the following per-unit profit for each plant–customer alternative.

	Customer 1	Customer 2	Customer 3	Customer 4
Plant 1	$15	$17	$18	$20
Plant 2	$17	$14	$19	$16
Plant 3	$18	$17	$17	$19

The manufacturing capacities during the current production period are: Plant 1, 5,000 units; Plant 2, 3,500 units; Plant 3, 4,000 units. The customer demands are: Customer 1, 1,500 units; Customer 2, 2,500 units; Customer 3, 4,000 units; Customer 4, 3,000 units. Develop a transportation model that WestFuel can use to determine how many units each plant should ship to each customer, with the goal of maximizing total profit. (As a hint, check the total production capacity and the total demand, and incorporate this information into the model as needed. you do not need to solve the LP

Answer 1

Let us suppose that

represents the fuel quantity supplied from plant i to customer j

let us consider the total quantity supplied by plant 1

Let us suppose total quantity received by customer

We have to maximize the profit

But we have also constraints which restricts upto some point

So total quantity supplied to customer will always less than or equal to total capacity of plant

Same type of constrain will be applicable to demand of customer

Total quantity supplied to customer will be less than or equal to demand of customer

So maximum profit using LP will be

an d functions will be