M L Aggarwal Solutions for Chapter: Application of Calculus in Commerce and Economics, Exercise 5: CHAPTER TEST

The cost function $C\left(x\right)$ for x breads is given by $C\left(x\right)=(3.5x+12000)$. If each bread is sold for $6$, determine the minimum number of breads that should be produced and sold to ensure no loss. 

The cost function $C\left(x\right)$ for $x$ breads is given by $C\left(x\right)=(3.5x+12000)$. If the selling price is$Rs 6.5$ per bread, what would be the break-even point? 

A factory is manufacturing table fans. From the information given below, calculate the breakeven point (of cost).
Total fixed cost $= 30 lacs$
Cost of labour per fan $= 30$
Cost of material per fan $= 275$
Miscellaneous variable expenses per fan $= 45$
Selling price per fan $= 500$. 

 The total/ cost of production and marketing x units of a product is given by $C\left(x\right)=\mathrm{Rs} \left(\frac{1}{3}{x}^3-10x^2+15x+30\right)$. Find the number of units of the product produced to minimise the marginal cost.

The total/cost of production and marketing $x$ units of a product is given by $C\left(x\right)=\mathrm{Rs} \left(\frac{1}{3}{x}^3- 10x^2+15x+10\right)$. Find the number of units of the product produced to minimize the average variable cost. 

If the demand function is $p=\sqrt{6-x}$. Find the level of production of output $x$ at which the total revenue will be maximum. 

The marginal cost function of a product is given by $MC=\frac{ 2}{\sqrt{4x+9}}$. If the fixed cost is $\mathrm{Rs} 540$, find the total cost function. Also find the average cost of producing $4$ units of the product. 

A cultural organisation is arranging a dance program. It expects $300$ persons to attend the show if the entrance fee is $8$ per person. It also estimated that if the entrance fee is decreased by $1$, then $60$ additional persons would attend the show. What should be the entrance fee to get the maximum revenue ?