‹ Back to the paper
Solve the following.
The marginal cost function of x units of a product is given by MC = 3x² - 10x + 3. The cost of…
The marginal cost function of $x$ units of a product is given by $\text{MC} = 3x^2 - 10x + 3$. The cost of producing one unit is ₹ 7. Find the total cost function and average cost function.
Answer
Answer
Integral: $\int \left(3x^2 - 10x + 3\right) dx$
$C(x) = \int MC\,dx = \int(3x^2-10x+3)\,dx = x^3-5x^2+3x+k$.
When $x=1$, $C=7$: $1-5+3+k = 7 \Rightarrow k=8$.
Total cost function: $C(x) = x^3-5x^2+3x+8$.
Average cost function: $AC = \frac{C(x)}{x}$
Hence $C(x) = x^3-5x^2+3x+8$ and $AC = x^2-5x+3+\frac8x$.
Final answer: $C(x)=x^3-5x^2+3x+8;\ AC=x^2-5x+3+\frac{8}{x}$