MCQ 11 Mark
Assertion (A): If the average cost (AC) of producing x units of an item is given by $AC =3 x ^2-7 x +5-\frac{11}{x}$, then the marginal cost (MC) of producing 5 units is ₹160.
Reason (R): $MC =\frac{d}{d x}( C )$.
Reason (R): $MC =\frac{d}{d x}( C )$.
- ✓Both A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer
View full question & answer→Correct option: A.
Both A and R are true and R is the correct explanation of A.
(a) Both A and R are true and R is the correct explanation of A.
Explanation: Given $A C=3 x^2-7 x+5-\frac{11}{x}$
Total cost C = AC * x
$\Rightarrow C=3 x^3-7 x^2+5 x-11$
$\begin{array}{l}\text { Now, Marginal Cost }( MC )=\frac{d}{d x} C=\frac{d}{d x}\left(3 x ^3-7 x ^2+5 x -11\right) \\ =9 x ^2-14 x +5 \\ {[ MC ]_{ X =5}=₹(9 \times 52-14 \times 5+5)=₹ 160}\end{array}$
$\therefore$ Both Assertion and Reason true. Reason is the correct explanation of Assertion.
Explanation: Given $A C=3 x^2-7 x+5-\frac{11}{x}$
Total cost C = AC * x
$\Rightarrow C=3 x^3-7 x^2+5 x-11$
$\begin{array}{l}\text { Now, Marginal Cost }( MC )=\frac{d}{d x} C=\frac{d}{d x}\left(3 x ^3-7 x ^2+5 x -11\right) \\ =9 x ^2-14 x +5 \\ {[ MC ]_{ X =5}=₹(9 \times 52-14 \times 5+5)=₹ 160}\end{array}$
$\therefore$ Both Assertion and Reason true. Reason is the correct explanation of Assertion.