Below is a question on limiting factor analysis and I cannot determine what the limitg factor is. Please help:

Short-term decisions Bolted Plc. Is a subsidiary of the JTX Group that manufactures a large range of screws. It is preparing its production plans for the next three months and has estimated the maximum demand from its customers to be 700 batches of BT1, 600 batches of BT2 and 550 batches of BT3.

These demand maximums are amended figures because a customer has just delayed its request for a large order and Bolted has unusually got some spare capacity over the next three months. However, these demand maximums do include a contract for the delivery of 90 batches of each to an important customer. If this minimum contract is not satisfied then Bolted Plc. Will have to pay a substantial financial penalty for non-delivery.

The Production Director is concerned at hearing news that two of the ingredients used are expected to be in short supply for the next three months. Bolted Plc. Does not hold inventory of these ingredients and although there are no supply problems for ingredient SE1, the supplies of ingredients SW1 and SW2 are expected to be limited to 22 760kgs of ingredient SW1 and 8 760kgs of ingredient SW2 respectively.

The Production Director has researched the problem and found that ingredient SQ1 can be used as a direct substitute for ingredient SW2. It also costs the same as ingredient SW2. There is an unlimited supply of ingredient SQ1


Screws BT1 BT2 BT3
$/Batch $/Batch $/Batch
Selling Price 2,700 3,600 2,100

Ingredient SE1 ($20/kg) 1,200 960 720
Ingredient SW1 ($40/kg) 560 720 320
Ingredient SW2 (&60/kg) 240 600 360

Labor ($28/hour) 84 112 168

Fixed cost absorbed 60 240 120



Required: Prepare calculations to determine the production mix that will maximise the profit of Bolted Plc. During the next three months.

Hi

If you calculate the total usage of SW1 you find out you go over the maximum amount available (14,000) by 14,600. Once you find that out you then need to calculate the return/kg and determine the optimum production. I got for BT1 (50), BT2(73.3) and BT3 (87.5) therefore we choose the highest value to go first into the production, which is BT3. Remembering that 90 batches have to be completed first for each product.

My final answer I got to was BT2 397 batches remainig and 790 batches remaining from BT1.

For the SW2 part since there is an unlimated amount of SQ1 that we can use instead. Therefore we would only need 5140kg.

If you want I can email you my working out.

To solve these problems you use least squares (optimisation) methodology