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Rate of Change, Marginal Cost & Revenue · Question 78 of 79

Question 78

HardOriginal question

Each unit sells at p=200−4xp = 200 - 4x rupees when xx units are sold, and the cost is C(x)=40x+500C(x) = 40x + 500 rupees. At what price is the profit greatest?

Options for question 78

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. P(x)=160x−4x2−500P(x) = 160x - 4x^{2} - 500, and P′(x)=160−8x=0P'(x) = 160 - 8x = 0 at x=20x = 20.

  2. The price there is 200−80=120200 - 80 = 120 rupees.

Worth noting

₹100 is the price that maximises revenue alone, at 25 units.

Concept
The price that maximises profit
Typical time
120 s
Your time
—
The rule this testsMaximising profit and revenue
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