CAT 2007QA Question 13

Graph & Maximum or Minimum value of Quadratic functionEasy
Passage / Data

Answer the next 2 questions based on the information given below.

Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2, where b and c are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by 66.66%. However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit.

What is the maximum daily profit, in rupees, that Mr. David can realize from his business?

Answer & solution

  • A

    620

  • B

    920

  • C

    840

  • 760

  • E

    Cannot be determined

Solution

Following from the first question, at x = 100 the profit is maximum.

At that level of production
​​​​​​​P(100) = –240 + 20 (100) – (100)2/10 = –240 + 2000 – 1000 = 760

Hence, option (d).

CAT 2007 QA Q13: What is the maximum daily profit, in rupees, that Mr. David can realize from his business? — Solution | TheCATExam