Question

Big Electronics manufactures two LED television monitors, identified as Model A and Model B. Big Electronics possesses three manufacturing plants. Each model has its lowest possible production cost when produced at Plant 1. However, Plant 1 does not have the capacity to handle the total production of both models. As a result, at least some of the production must be routed to the other two manufacturing plants. The following table shows the minimum production requirements for next month, the plant capacities in units per month, and the production cost per unit at each plant:

Model	Production Cost per Unit			Minimum Production Requirements
	Plant 1	Plant 2	Plant 3
A	$30	$55	$40	70,000
B	$25	$45	$65	60,000
Production Capacity	80,000	50,000	40,000

Big's objective is to determine the minimum cost production plan.

1. Develop the generic model.

Answer 1

To determine the minimum cost production plan - we need to understand the least cost that is going to be incurred.

Based on the facts given, model B has the least price if produced in plant 1. Also, as Plant 1 has a capacity if 80,000 units and the requirement of Model B is only 60,000 units, we know clearly that it's best to produce 100% of Model B's requirement from Plant 1 as it's the cheapest. Now, after producing 60,000 units, Plant 1 still has the capacity to produce Model A which has it's lowest cost of production too in Plant 1. Hence, we utilize the 20,000 units from Plant 1 to produce Model A. Now that Plant 1 has reached it's fullest capacity, the remaining 50,000 units of would be produced as - 40,000 units would be from Plant 3, which is the next lowest cost and the remaining 10,000 units from Plant 2.

The formula would be as below -

Model B - 60,000 * $25 = 1,500,000

Model A - 20,000 * $30 = 600,000; 40,000 * $40 = 1,600,000 and 10,000 * $55 = 550,000

Hence, the total minimum cost of production = $4,250,000