One part of managerial accounting is the need to understand limiting factor for short term decision. As a result of limited supply of resources constraint, a company normally cannot produces as many products as it wish.
The limited supply of resources can be in many forms like limited cash, labor time, material/machine availability and others.
In line with the limited resources, the production manager therefore needs to plan the production mix in order to maximize its profit.
To establish the proper production mix, the rule is to rank the products according to the:
CONTRIBUTION PER LIMITING FACTOR
Whichever product that gives the highest UCM per LF will given the highest rank.
The highest rank will be given the highest priority to be produced using the available resources.
The remaining resources will then be used to produce the next ranking products until all the resources are used up.
The below illustration assumes a shortage of direct labor as the limiting resource constraint.
The details of the company three product lines are as follows:
Products A B C
Selling price: $50 $40 $30
Variable costs : $20 $20 $20
Unit Contribution: $30 $20 $10
Expected demand 1,000units;500units; 600units
To produce 1 unit of product, the direct labor hours for each product is:
Product A : 10 hours; Product B : 5 hour Product C: 1 hour
Due to unavailability of labor supply, for the forthcoming period, it is assumed that the overall shortage of labor hours is 1,100 hours.
Question: Determine the production mix to maximize the company’s profit.
(1) Compute the Contribution per limiting factor
Contribution per Limiting Factor
=Unit Contribution/ No of hour to make the product
Product A:Unit Contribution $30 /10 hours = 3
Product B:Unit Contribution $20/5 hour = 4
Product C: Unit Contribution $10/1 hour =10
(2) Rank the Contribution per limiting factor ( highest ratio of contribution per limiting factor)
Product A =Rank No 3
Product B =Rank No 2
Product C =Rank No 1
(3) Determine the overall total hours to produce ALL products A,B & C and what is the shortage:
= Expected demand x No of hours
Product A=1,000 units x 10hours =10,000 hours
Product B=500 units x 5 hour = 2,500 hours
Product C=600 units x 1 hour = 600 hours
Total Direct Hours to produce All products =13,100
Total Available hours due to constraint =12,000
Shortage of (1,100) hours
(4) Using the Rank as per item 2 ,do the allocation of the available 12,000 ( 1,100 hours shortage) :
Total labor available = 12,000
Rank No 1: Product C = (600)hours =600 units
Rank No.2 :Product B =(2,500)hours =500 units
Rank No 3: Product C =(8,900)hours =8,900/10=890 units
Therefore the appropriate production mix is:
Product C: 600 units
Product B: 500 units
Product A: 890 units