The marginal cost of making $x$ units is $3x^{2} - 10x + 15$ rupees, and the fixed cost is ₹400. What is the total cost function?

x^{3} - 5 x^{2} + 15 x

Correct answerYour answer

x^{3} - 5 x^{2} + 15 x + 400

Correct answerYour answer

6 x + 390

Correct answerYour answer

x^{3} - 10 x^{2} + 15 x + 400

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Total cost is the integral of marginal cost: $C(x) = x^{3} - 5x^{2} + 15x + k$ .
The constant is the fixed cost, $C(0) = 400$ : $C(x) = x^{3} - 5x^{2} + 15x + 400$ .

Worth noting

Without the 400 the cost of making nothing would be zero, but the fixed cost is paid anyway.

Ten questions from Consumer & Producer Surplus, at your own pace.

The marginal cost of making xxx units is 3x2−10x+153x^{2} - 10x + 153x2−10x+15 rupees, and the fixed cost is ₹400. What is the total cost function?