CAT 2025 Lesson : Data Tables - Case 4

Answer questions 10 to 13 based on the following information:

The following table shows the break-up of actual costs incurred by a company in last five years (year 2002 to year 2006) to produce a particular product:



The production capacity of the company is 2000 units. The selling price for the year 2006 was Rs. 125 per unit. Some costs change almost in direct proportion to the change in volume of production, while others do not follow any obvious pattern of change with respect to the volume of production and hence are considered fixed. Using the information provided for the year 2006 as the basis for projecting the figures for the year 2007, answer the following questions.
[CAT 2007]

10) What is the approximate cost per unit in rupees, if the company produces and sells 1400 units in the year 2007?

(1) 104
(2) 107
(3) 110
(4) 115
(5) 116

11) What is the minimum number of units that the company needs to produce and sell to avoid any loss?

(1) 313
(2) 350
(3) 384
(4) 747
(5) 928

12) If the company reduces the price by 5%, it can produce and sell as many units as it desires. How many units the company should produce to maximize its profit?

(1) 1400
(2) 1600
(3) 1800
(4) 1900
(5) 2000

13) 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?

(1) 25,400
(2) 24,400
(3) 31,400
(4) 32,900
(5) 32,000

Solution

10)

Observing values in the table, we can conclude that material, labour and operating cost is directly proportional to the change in volume of production. The other costs are fixed costs.

If $x$ is the number of units produced in 2007, then total cost of the production will be $100x$.

The variable cost for material, labour, and operation is $50x$, $20x$, and $30x$ respectively. Total fixed cost (using information for 2006) = 1400 + 1200 + 400 + 800 + 5800 = 9600.

Therefore, the total cost of the production = $100x + 9600$.

Average cost / unit = $\dfrac{TC}{no \ of \ items}$

$x = 1400$
Average cost = $\dfrac{1400 \times 100 + 9600}{1400} = 106.85$

Answer: (2) 107

11)

To avoid any loss the total revenue should be equal to the total cost of the production.

Let $x$ be the units that are produced.

Revenue = $125x$
Total cost of the production = $100x + 9600$

⇒ $125x = 100x + 9600$

⇒ $25x = 9600$

⇒ $x = 384$

Answer: (3) 384

12)

The new price = $0.95 \times 125 = 118.75$

Profit = $118.75x - 100x - 9600$= $18.75x - 9600$

If profit should be maximum then $18.75x$ should be maximum. As maximum production is 2000 units, profit is maximised when 2000 units are produced.

Answer: (5) 2000

13)

If company sells a maximum of 1400 units, then revenue is fixed at Rs. 125/unit. If more than 1400 units need to be sold then revenue must be reduced to Rs. 120/unit. Since the company cannot sell more than 1700 units.

Therefore, the maximum profit the company can earn is 25,400.

Answer: (1) 25,400

Answer:
10) (2) 107
11) (3) 384
12) (5) 2000
13) (1) 25,400