Find the area bounded by y = x between the lines x = −1 and x = 2 with x -axis.

Find the area bounded by the line y = x, the x-axis and the ordinates x = 1, x = 2

Using integration, find the area of the region bounded by the line y −1 = x, the x axis and the ordinates x = –2, x = 3.

Find the area of the region lying in the first quadrant bounded by the region y = 4x², x = 0, y = 0 and y = 4

The marginal cost function of manufacturing x shoes is 6 +10x − 6x². The cost producing a pair of shoes is Rs. 12. Find the total and average cost function.

A company has determined that the marginal cost function for a product of a particular commodity is given by MC = 125 +10x - \(\frac{x^2}{9}\) where C rupees is the cost of producing x units of the commodity. If the fixed cost is Rs.250 what is the cost of producing 15 units.

The marginal cost function MC = 2 + 5e^x Find C if C (0)=100

The rate of new product is given by f (x) = 100 − 90 e^−x where x is the number of days the product is on the market. Find the total sale during the first four days. (e^–4 = 0.018)

A company produces 50,000 units per week with 200 workers. The rate of change of productions with respect to the change in the number of additional labour x is represented as 300 - 5x^2/3. If 64 additional labours are employed, find out the additional number of units, the company can produce.

The price of a machine is 6,40,000 if the rate of cost saving is represented by the function f(t) = 20,000 t. Find out the number of years required to recoup the cost of the function.

For the marginal revenue function MR = 35 + 7x − 3x², find the revenue function and demand function.

A company receives a shipment of 200 cars every 30 days. From experience it is known that the inventory on hand is related to the number of days. Since the last shipment, I(x)=200 − 0.2x. Find the daily holding cost for maintaining inventory for 30 days if the daily holding cost is Rs. 3.5

Mr. Arul invests Rs. 10,000 in ABC Bank each year, which pays an interest of 10% per annum compounded continuously for 5 years. How much amount will there be after 5 years.(e^0.5 = 1.6487)

The cost of over haul of an engine is Rs. 10,000 The operating cost per hour is at the rate of 2x − 240 where the engine has run x km. Find out the total cost if the engine run for 300 hours after overhaul.

In year 2000 world gold production was 2547 metric tons and it was growing exponentially at the rate of 0.6% per year. If the growth continues at this rate, how many tons of gold will be produced from 2000 to 2013? [e^0.078 = 1.0811)

A company receives a shipment of 500 scooters every 30 days. From experience it is known that the inventory on hand is related to the number of days x. Since the shipment, I (x) = 500 − 0.03x², the daily holding cost per scooter is Rs. 0.3. Determine the total cost for maintaining inventory for 30 days.

An account fetches interest at the rate of 5% per annum compounded continuously An individual deposits Rs. 1,000 each year in his account. How much will be in the account after 5 years.(e^0.25 = 1.284)

The marginal cost function of a product is given by \(\frac { dC }{ dx } \) = 100 −10x + 0.1x² where x is the output. Obtain the total and the average cost function of the firm under the assumption, that its fixed cost is Rs. 500.

The marginal cost function is MC = 300 \({ x }^{ \frac { 2 }{ 5 } }\) and fixed cost is zero. Find out the total cost and average cost functions.

If the marginal cost function of x units of output is \(\frac { a }{ \sqrt { ax+b } } \) and if the cost of output is zero. Find the total cost as a function of x.

Determine the cost of producing 200 air conditioners if the marginal cost (is per unit) is C' (x) = \(\frac { { x }^{ 2 } }{ 200 } \) + 4

The marginal revenue (in thousands of Rupees) functions for a particular commodity is 5 + 3 ^{−0 03} e. x where x denotes the number of units sold. Determine the total revenue the sale of 100 units. (Given e ^-0.03x = 0.05 approximately)

If the marginal revenue function for a commodity is MR = 9 − 4x². Find the demand function.

Given the marginal revenue function \(\frac { 4 }{ ({ 2x+3 })^{ 2 } } \)-1, show that the average revenue function is P = \(\frac { 4 }{ 6x+9 } \)-1

If the marginal revenue function is R'(x) = 1500 − 4x − 3x². Find the revenue function and average revenue function.

Find the revenue function and the demand function if the marginal revenue for x units is MR = 10 + 3x − x².

The marginal cost function of a commodity is given by MC = \(\frac { 14000 }{ \sqrt { 7x+4 } } \) and the fixed cost is Rs. 18,000. Find the total cost and average cost.

If MR = 14 − 6x + 9x², find the demand function.

The demand function of a commodity is y = 36 − x². Find the consumer’s surplus for y₀ = 11

Find the producer’s surplus defined by the supply curve g(x) = 4x + 8 when x_o= 5.

Calculate consumer’s surplus if the demand function p = 50 − 2x and x = 20

Calculate consumer’s surplus if the demand function p = 122 − 5x − 2x² and x = 6

The demand function p = 85 − 5x and supply function p = 3x − 35. Calculate the equilibrium price and quantity demanded. Also calculate consumer’s surplus.

The demand function for a commodity is p = e^−x. Find the consumer’s surplus when p = 0.5.

Calculate the producer’s surplus at x = 5 for the supply function p = 7 + x.

If the supply function for a product is p = 3x + 5x². Find the producer’s surplus when x = 4.

The demand function for a commodity is p = \(\frac { 36 }{ x+4 } \). Find the consumer’s surplus when the prevailing market price is Rs. 6.

The demand and supply functions under perfect competition are p_d = 1600 − x² and p_s = 2x² + 400 respectively. Find the producer’s surplus.

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.

A company has determined that marginal cost function for x product of a particular commodity is given by MC = 125 +10x − \(\frac { { x }^{ 2 } }{ 9 } \). Where C is the cost of producing x units of the commodity. If the fixed cost is Rs. 250 what is cost of producing 15 units

The marginal revenue function for a firm is given by MR = \(\frac { 2 }{ x+3 } -\frac { 2x }{ { \left( x+3 \right) }^{ 2 } } +5\). Show that the demand function is \(P=\frac{2}{x+3}+5\)

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

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

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

The marginal cost function MC = 2 + 5e^x Find AC.