Determine the Single Limiting Factor
A company manufactures and sells three products as A, B and C. The unit cost and revenue structure for every product and its maximum forecast demand for the coming period are given as:
|
Product
|
A
|
B
|
C
|
|
Selling price per unit (Shs.)
|
140
|
100
|
120
|
|
Variable cost per unit (Shs.)
|
70
|
60
|
80
|
|
Maximum demand (units)
|
500
|
300
|
300
|
|
Machine hours required per unit
|
10
|
4
|
5
|
The company has a maximum of 6000 machine hours available throughout the coming period
Required
1. Estimate the number of units of each product A, B, and C that should be produced and sold in order to maximize profit
2. Estimate the maximum profit earned from the decision strategy per 1
3. Suggest other factors that management may wish to consider such could result in a change in their decision
4. Estimate the product units to be produced and sold and the net profit earned whether the company wishes to maximize sales of product A since it is thought to be a future market leader
5. Estimate the product units to be sold and the net profit earned it the company agrees to produce a minimum of 70 percent of the maximum demand of every product in order to maintain market spread.
Solution
|
|
A
|
B
|
C
|
Total
|
|
Maximum demand (units)
|
500
|
300
|
300
|
|
|
Machine hours per unit
|
10
|
4
|
5
|
|
|
Machine hours required
|
5000
|
1200
|
1500
|
7700
|
|
Machine hours available
|
|
|
|
6000
|
|
Shortfall
|
|
|
|
1700
|
The specified calculation confirms that machine time is a limiting factor that will restrict the number of products that can be produced and sold
|
Product
|
A
|
B
|
C
|
Total
|
|
Contribution per unit (Shs.)
|
70
|
40
|
40
|
|
|
Contribution per machine hr (Shs.)
|
70
|
10
|
8
|
|
|
Product ranking
|
(3)
|
(1)
|
(2)
|
|
|
Machine hours utilized
|
3300
|
1200
|
1500
|
|
|
1. Product units produced and sold
|
330
|
300
|
300
|
|
|
Contribution earned (Shs.)
|
23100
|
12000
|
12000
|
47100
|
|
Less fixed cost
|
|
|
|
20000
|
|
2. Net profit
|
|
|
|
22710
|
3. The profit maximizing mix may not be implemented where management wish to keep a more balanced market mix or wherever they wish to concentrate on a future market leader. In addition they may wish to explore the possibility of sub contracting some production or of acquiring additional machinery either part of a long term expansion of capacity or on hire
4. Where the sales of product A are to be maximized since it is considered that it will be a future market leader, the analysis sequence is as:
a) Employ the machine hours essential to maximize production of A that is 500 units x 10 hour = 5000 hours
b) Employ the keeping 1000 machine hours to produce B and C in their ranking order
Product B has a higher contribution per machine hour. The 1000 machine hours available are enough to produce 1000/4 = 250 units of B. It is less than its maximum demand. There are no hours left in that to produce product C. Therefore the sales and profit strategy is as:
|
|
Units
|
Contribution per unit Shs.
|
Total
|
|
Product A
|
500
|
70
|
35000
|
|
Product B
|
280
|
40
|
10000
|
|
Product C
|
Nil
|
|
|
|
|
|
|
45000
|
|
Less fixed cost
|
|
|
20000
|
|
Net profit
|
|
|
25000
|
5. Where sales have to be spread in order to satisfy 70 percent of the maximum demand of every product like the first criterion the analysis sequence is
a) Employ the machine hours required to produce 70 percent of the maximum production of every product
b) Employ the residual hours up to the maximum of 6000 hours to produce additional units of the product in their ranking up to the maximum demand in every case so long as it is possible
|
|
A
|
B
|
C
|
Total
|
|
Maximum units
|
500
|
300
|
300
|
|
|
70% of max units
|
350
|
210
|
210
|
|
|
Machine hours
|
3500
|
840
|
1050
|
5390
|
|
Residual hours usage
|
-
|
360
|
250
|
610
|
|
Total machine hours used
|
3500
|
1200
|
1300
|
6000
|
|
Total units
|
350
|
300
|
260
|
|
|
Total contribution Shs.
|
|
|
|
|
|
|
24500
|
12000
|
10400
|
46900
|
|
Less fixed cots
|
|
|
|
20000
|
|
Net profit
|
|
|
|
26900
|