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Rate of Change, Marginal Cost & Revenue · Question 74 of 79

How many cakes a day give the bakery the greatest profit?

Question 74

MediumOriginal question

A home bakery's cost of making xx cakes a day is C(x)=200+10x+0.5x2C(x) = 200 + 10x + 0.5x^{2} rupees. Every cake sells for ₹50, however many she makes.

How many cakes a day give the bakery the greatest profit?

Options for question 74

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. P(x)=50x−200−10x−0.5x2=40x−200−0.5x2P(x) = 50x - 200 - 10x - 0.5x^{2} = 40x - 200 - 0.5x^{2}.

  2. P′(x)=40−x=0P'(x) = 40 - x = 0 at x=40x = 40, and P′′(x)=−1<0P''(x) = -1 < 0: a maximum. This is where marginal cost reaches the ₹50 price.

Worth noting

20 cakes is where the average cost is least, not where profit is greatest.

Concept
Profit is greatest where MR = MC
Typical time
120 s
Your time
—
The rule this testsMaximising profit and revenue
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