M L Aggarwal Solutions for Chapter: Application of Calculus in Commerce and Economics, Exercise 3: EXERCISE

The cost function $C\left(x\right)$ of a firm is given by $C\left(x\right)=2x^2-4x+5$. Find the average cost when $x=10$.

The cost function $C\left(x\right)$ of a firm is given by $C\left(x\right)=2x^2-4x+5$. Find the marginal cost when $x = 10$. 

A monopolist's demand function is $x=50-\frac{p}{4}$. At what price is marginal revenue zero ?

The total revenue in rupees received from the sale of $x$ units of a product is given by $R\left(x\right)=300x-\frac{x^2 }{5}$. Find the total revenue when $MR = 0$.

The demand function of a monopolist is $P\left(x\right)=300-x^2$ Find the output $x$ when revenue is maximum. 

A product can be manufactured at a total cost $C\left(x\right)=\frac{x^2}{100}+100x+40$, where $x$ is the number of units produced. The price at which each unit can be sold is given by $P\left(x\right)=200-\frac{x}{400}$. Determine the production level $x$ at which the profit is maximum. What is the price per unit and total profit at this level of production?

A manufacturer can produce x items at a total cost of Rs. $\left(120x+\frac{x^2}{2}\right)$ . If he sells the whole produce at $p$ per item, where
$p = 2 \left(100-\frac{x}{4}\right)$, then find the production level x at which the profit is maximum. What is the price per item and the total profit? 

Find the profit maximising output level, given $x=200-10p$  and $AC=10+\frac{7}{30}x$    where x represents the units of output, $p$ is the price per unit and $AC$ is the average cost.