Miscellaneous problems

Miscellaneous problems

1. A manufacture’s marginal revenue function is given by MR= 275 − x − 0.3x2 . Find the increase in the manufactures total revenue if the production is increased from 10 to 20 units.

2. A company has determined that marginal cost function for x product of a particular commodity is given by MC = 125 + 10x − x2/9 . Where C is the cost of producing x units of the commodity. If the fixed cost is ₹ 250 what is cost of producing 15 units

3. The marginal revenue function for a firm is given by MR= . Show that the demand function is P = 2/[ x + 3] + 5.

4. For the marginal revenue function MR = 6 − 3x2 âˆ’ x3 , Find the revenue function and demand function.

5. The marginal cost of production of a firm is given by C ′ ( x) = 20 + x/20 the marginal revenue is given by R ′ ( x) = 30 and the fixed cost is ₹ 100. Find the profit function.

6. The demand equation for a product is pd = 20 − 5x and the supply equation is ps = 4x + 8. Determine the consumer’s surplus and producer’s surplus under market equilibrium.

7. A company requires f(x) number of hours to produce 500 units. It is represented by f (x) = 1800x−0.4 . Find out the number of hours required to produce additional 400 units. [(900)0.6=59.22, (500)0.6=41.63]

8. The price elasticity of demand for a commodity is p/x3 . Find the demand function if the quantity of demand is 3, when the price is ₹2.

9. Find the area of the region bounded by the curve between the parabola y = 8x2 âˆ’ 4x + 6 the y-axis and the ordinate at x = 2.

10. Find the area of the region bounded by the curve y2 = 27x3 and the lines x = 0, y = 1 and y = 2.

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