11th Business Maths Monthly Test - 4 ( Applications of Differentiation )

MABS Institution

11th Business Maths Monthly Test - 4 ( Applications of Differentiation )-Aug 2020

Time : 2.00 Hours

Part - A

Generic 5 - Answer All Question

The total cost function of a firm C(x) = \(\frac { { x }^{ 3 } }{ 3 } -{ 5x }^{ 2 }+28x+10\), where x is the output. A tax at the rate of Rs. 2 per unit of output is imposed and the producer adds it to his cost. If the market demand function is given by p = 2530 – 5x, where p is the price per unit of output, find the profit-maximizing the output and price.

A monopolist has a demand curve x = 106 – 2p and average cost curve AC = 5+\(\frac { x }{ 50 } \) where p is the price per unit output and x is the number of units of output. If the total revenue is R = px, determine the most profitable output and the maximum profit.

For the cost function \(C=2x\left(x+5\over x+2\right)+7\), prove that marginal cost (MC) falls continuously as the output x increases

For the cost function C= 2000 + 1800x - 75x² + x³, discuss the behaviour of the marginal cost function.

The relationship between Profit P and advertising cost x is given by \(P={4000x\over 500+x}-x\) . Find x which maximises P.

Find the stationary values and stationary points for the function f(x) = 2x³ +9x² +12x+1

The demand and the cost function of a firm are p = 497-0.2x and C = 25x+10000 respectively. Find the output level and price at which the profit is maximum

Verify the relationship of elasticity of demand, average revenue and marginal revenue for the demand law p = 50-3x.

The following table gives the annual demand and unit price of 3 items

Items Annual Demand (units) Unit Price Rs

A 800 0.02

B 400 1.00

C 13,800 0.20

Ordering cost is Rs. 5 per order and holding cost is 10% of unit price.
Determine the following:
(i) EOQ in units
(ii) Minimum average cost
(iii) EOQ in rupees
(iv) EOQ in years of supply
(v) Number of orders per year.

Items	Annual Demand (units)	Unit Price Rs
A	800	0.02
B	400	1.00
C	13,800	0.20

Let u = log\(\frac { { x }^{ 4 }+{ y }^{ 4 } }{ x+y } \). By using Euler’s theorem show that \(x.\frac { \partial u }{ \partial x } +y.\frac { \partial u }{ \partial y } =3\) .

A company uses 48000 units of a raw material costing ` 2.5 per unit. Placing each order costs Rs. 45 and the carrying cost is 10.8 % per year of the average inventory. Find the EOQ, total number of orders per year and time between each order. Also verify that at EOQ carrying cost is equal to ordering cost.

A firm has revenue function R = 8x and production cost function \(C = 150000 + 60\left(x^2\over 900\right)\) Find the total profit function and the number of units to be sold to get the maximum profit.

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11th Business Maths Monthly Test - 4 ( Applications of Differentiation )

MABS Institution

11th Business Maths Monthly Test - 4 ( Applications of Differentiation )-Aug 2020

Part - A

Generic 5 - Answer All Question

A monopolist has a demand curve x = 106 – 2p and average cost curve AC = 5+\(\frac { x }{ 50 } \) where p is the price per unit output and x is the number of units of output. If the total revenue is R = px, determine the most profitable output and the maximum profit.

For the cost function \(C=2x\left(x+5\over x+2\right)+7\), prove that marginal cost (MC) falls continuously as the output x increases

For the cost function C= 2000 + 1800x - 75x2 + x3, discuss the behaviour of the marginal cost function.

The relationship between Profit P and advertising cost x is given by \(P={4000x\over 500+x}-x\) . Find x which maximises P.

Find the stationary values and stationary points for the function f(x) = 2x3 +9x2 +12x+1

The demand and the cost function of a firm are p = 497-0.2x and C = 25x+10000 respectively. Find the output level and price at which the profit is maximum

Verify the relationship of elasticity of demand, average revenue and marginal revenue for the demand law p = 50-3x.

Let u = log\(\frac { { x }^{ 4 }+{ y }^{ 4 } }{ x+y } \). By using Euler’s theorem show that \(x.\frac { \partial u }{ \partial x } +y.\frac { \partial u }{ \partial y } =3\) .

A firm has revenue function R = 8x and production cost function \(C = 150000 + 60\left(x^2\over 900\right)\) Find the total profit function and the number of units to be sold to get the maximum profit.

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Tamilnadu Stateboardszs - Class

For the cost function C= 2000 + 1800x - 75x² + x³, discuss the behaviour of the marginal cost function.

Find the stationary values and stationary points for the function f(x) = 2x³ +9x² +12x+1