Question

Given that the company cannot sell more than 1700 units and it will have to reduce the price by Rs. 5 for all units if it wants to sell more than 1400 units. What is the maximum profit, in rupees, that the company can earn?

• A. 25,400
• B. 24,400
• C. 31,400
• D. 32,000

Answer 1

The correct option is A 25,400

Looking at the values in the table, one can easily conclude that the costs which are directly proportional to the change in volume of production are 'material', 'labour' and 'operating' cost of machines'. Rest of the costs are all fixed costs. If 'x' is the number of units produced in 2007 then the total cost of production would be
C=9600 (Fixed cost) + 100x(Variable cost)
Variable cost = 100x because as the number of units for 2006 is 1200 and variable cost for that is 120000 i.e. 100 times the number of units.
If the company sells a maximum of 1400 units, the selling price is fixed at Rs. 125 per unit. If more than 1400 units are sold, the selling price is reduced to Rs. 120 per unit. The company cannot sell more than 1700 units.
To earn the maximum profit at a unit selling price of Rs. 125, the company must sell 1400 units. The maximum profit earned, denoted by $P_0$, is calculated as below:
$P_0=125\times 1400-(9600+100\times 1400)=Rs.25400$
Now, if the company sells 'x' number of units. (x> 1400) then the profit earned will be:
$P_x=120x-(9600+100x)=20x-9600$
The minimum value of x for which $P_x$ will be more than $P_0$ must satisfy the following inequality:
$20x-9600>25400\Rightarrow x>1750$
As only a maximum of 1700 units can be sold, $P_x$ will never be more than $P_0$. Hence the maximum profit that can be earned is Rs. 25400 only.