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Rate of Change, Marginal Cost & Revenue · Question 66 of 79

Question 66

MediumOriginal question

For xx units, revenue is R(x)=60x−x2R(x) = 60x - x^{2} rupees and cost is C(x)=12x+100C(x) = 12x + 100 rupees. What is the greatest profit the firm can make?

Options for question 66

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. P(x)=48x−x2−100P(x) = 48x - x^{2} - 100; P′(x)=48−2x=0P'(x) = 48 - 2x = 0 at x=24x = 24.

  2. P(24)=1,152−576−100=476P(24) = 1{,}152 - 576 - 100 = 476 rupees.

Worth noting

₹576 forgets the fixed cost of ₹100.

Concept
The greatest profit
Typical time
90 s
Your time
—
The rule this testsMaximising profit and revenue
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