12th Business Maths Weekly Test - 2 ( Integral Calculus – II )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 2 ( Integral Calculus – II )-Aug 2020

Time : 2.00 Hours

Part - A

Generic 2 - Answer All Question

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.

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

The elasticity of demand with respect to price for a commodity is given by \(\frac{(4-x)}{x}\), where p is the price when demand is x. Find the demand function when price is 4 and the demand is 2. Also find the revenue function.

A firm’s marginal revenue function is MR = 20e^-x/10 \(\left( 1-\frac { x }{ 10 } \right) \). Find the corresponding demand function.

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

The demand and supply functions under perfect competition are p₄= 1600 − x² and p_s = 2x² + 400 respectively. Find the producer’s surplus.

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.

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.

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⁻³= 0.05 approximately)

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

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

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.

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.

The marginal cost of production of a firm is given by C'(x) = 5 + 0.13x , the marginal revenue is given by R'(x) = 18 and the fixed cost is Rs. 120. Find the profit function.

Under perfect competition for a commodity the demand and supply laws are P_d= \(\frac { 8 }{ x+1 } -2\) and P_s= \(\frac { x-3 }{ 2 } \) respectively. Find the consumer’s and producer’s surplus.

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

Calculate the area bounded by the parabola y² = 4ax and its latusrectum.

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

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

If MR = 20 − 5x + 3x², find total revenue 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

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.

Find the area bounded by the lines y − 2x − 4 = 0, y = 1, y = 3 and the y-axis

If the marginal cost (MC) of a production of the company is directly proportional to the number of units (x) produced, then find the total cost function, when the fixed cost is Rs. 5,000 and the cost of producing 50 units is Rs. 5,625.

Elasticity of a function \(\frac{Ey}{Ex}\) is given by \(\frac{Ey}{Ex}\) = \(\frac { -7x }{ (1-2x)(2+3x) } \). Find the function when x = 2, y = \(\frac{3}{8}\)

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12th Business Maths Weekly Test - 2 ( Integral Calculus – II )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 2 ( Integral Calculus – II )-Aug 2020

Part - A

Generic 2 - Answer All Question

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.

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

The elasticity of demand with respect to price for a commodity is given by \(\frac{(4-x)}{x}\), where p is the price when demand is x. Find the demand function when price is 4 and the demand is 2. Also find the revenue function.

A firm’s marginal revenue function is MR = 20e-x/10 \(\left( 1-\frac { x }{ 10 } \right) \). Find the corresponding demand function.

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

The demand and supply functions under perfect competition are p4 = 1600 − x2 and ps = 2x2 + 400 respectively. Find the producer’s surplus.

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.

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.

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−3 = 0.05 approximately)

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

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

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.

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.

The marginal cost of production of a firm is given by C'(x) = 5 + 0.13x , the marginal revenue is given by R'(x) = 18 and the fixed cost is Rs. 120. Find the profit function.

Under perfect competition for a commodity the demand and supply laws are Pd = \(\frac { 8 }{ x+1 } -2\) and Ps = \(\frac { x-3 }{ 2 } \) respectively. Find the consumer’s and producer’s surplus.

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

Calculate the area bounded by the parabola y2 = 4ax and its latusrectum.

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

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

If MR = 20 − 5x + 3x2, find total revenue 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

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.

Find the area bounded by the lines y − 2x − 4 = 0, y = 1, y = 3 and the y-axis

If the marginal cost (MC) of a production of the company is directly proportional to the number of units (x) produced, then find the total cost function, when the fixed cost is Rs. 5,000 and the cost of producing 50 units is Rs. 5,625.

Elasticity of a function \(\frac{Ey}{Ex}\) is given by \(\frac{Ey}{Ex}\) = \(​​\frac { -7x }{ (1-2x)(2+3x) } \). Find the function when x = 2, y = \(\frac{3}{8}\)

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

A firm’s marginal revenue function is MR = 20e^-x/10 \(\left( 1-\frac { x }{ 10 } \right) \). Find the corresponding demand function.

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

The demand and supply functions under perfect competition are p₄= 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.

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⁻³= 0.05 approximately)

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

Under perfect competition for a commodity the demand and supply laws are P_d= \(\frac { 8 }{ x+1 } -2\) and P_s= \(\frac { x-3 }{ 2 } \) respectively. Find the consumer’s and producer’s surplus.

Calculate the area bounded by the parabola y² = 4ax and its latusrectum.

If MR = 20 − 5x + 3x², find total revenue function.

Elasticity of a function \(\frac{Ey}{Ex}\) is given by \(\frac{Ey}{Ex}\) = \(\frac { -7x }{ (1-2x)(2+3x) } \). Find the function when x = 2, y = \(\frac{3}{8}\)