The total cost function for production and marketing of a product is given by , where is the number…
The total cost function for production and marketing of a product is given by $C(x) = \frac{3x^2}{4} - 7x + 3$, where $x$ is the number of units produced.
Find the level of output (number of units produced) for which $MC = AC$.
Answer
Answer
AIWritten by AI (gemini-2.5-pro) - it can contain mistakes.
Given $C(x) = \frac{3x^2}{4} - 7x + 3$.
$MC = C'(x) = \frac{3}{2}x - 7$.
$AC = \frac{C(x)}{x} = \frac{3x}{4} - 7 + \frac{3}{x}$.
Setting $MC = AC$:
$\frac{3}{2}x - 7 = \frac{3x}{4} - 7 + \frac{3}{x} \implies \frac{3}{4}x = \frac{3}{x} \implies x^2 = 4$.
Since output $x > 0$, $x = 2$ units.
From ISC 2026 Mathematics Paper 1, question 19(v).