A manufacturer can sell x items at a price of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $S(x)$ be the total revenue from selling $x$ items and $C(x)$ be the cost price of $x$ items. Then,$S(x) = x \left(5 - \frac{x}{100}\right) =

Vedclass · Accepted Answer

$240$

Vedclass · Answer

(A) Let $S(x)$ be the total revenue from selling $x$ items and $C(x)$ be the cost price of $x$ items. Then,$S(x) = x \left(5 - \frac{x}{100}ight) = 5x - \frac{x^2}{100}$. The cost function is $C(x) = \frac{x}{5} + 500$. The profit function $P(x)$ is defined as $P(x) = S(x) - C(x)$. $P(x) = \left(5x - \frac{x^2}{100}ight) - \left(\frac{x}{5} + 500ight) = 5x - \frac{x^2}{100} - 0.2x - 500 = 4.8x - \frac{x^2}{100} - 500$. To find the maximum profit,we find the derivative $P'(x)$ and set it to zero: $P'(x) = 4.8 - \frac{2x}{100} = 4.8 - \frac{x}{50}$. Setting $P'(x) = 0$,we get $4.8 = \frac{x}{50}$,which implies $x = 4.8 	imes 50 = 240$. To verify it is a maximum,we check the second derivative $P''(x) = -\frac{1}{50}$. Since $P''(240) = -\frac{1}{50} < 0$,the profit is maximum at $x = 240$.

$A$ manufacturer can sell $x$ items at a price of rupees $\left(5 - \frac{x}{100}\right)$ each. The cost price of $x$ items is $\text{Rs} \left(\frac{x}{5} + 500\right)$. Find the number of items he should sell to earn maximum profit.

Similar Questions

An enemy Apache helicopter is flying along the curve given by $y = x^{2} + 7$. $A$ soldier,placed at $(3, 7)$,wants to shoot down the helicopter when it is nearest to him. Find the nearest distance.

What are the minimum and maximum values of the function $f(x) = x^5 - 5x^4 + 5x^3 - 10$?

$A$ manufacturer produces $x$ items per week at a total cost of Rs $(x^2+78x+2500)$. The price per unit is given by $8x = 600 - p$,where $p$ is the price of each unit. Then the maximum profit obtained is

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x)=|x|+|x^2-1|$. The total number of points at which $f$ attains either a local maximum or a local minimum is

Let $f(x) = \int_{0}^{x} e^{x+t} dt$. Then the abscissa of the point where the tangent to $f(x)$ is parallel to the $x$-axis is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module