11th Business Maths Weekly Test - 2 ( Applications of Differentiation )

MABS Institution

11th Business Maths Weekly Test - 2 ( Applications of Differentiation )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

For the demand function p = 550–3x– 6x² where x is quantity demand and p is unit price. Show that MR = \(p\left[ 1-\frac { 1 }{ { n }_{ d } } \right] \)

A tour operator charges Rupees 136 per passenger with a discount of 40 paisa for each passenger in excess of 100. The operator requires at least 100 passengers to operate he tour. Determine the number of passenger that will maximize the amount of money the tour perator receives.

The demand for a quantity A is q=13 - 2P₁ - \({ 3p }_{ 2 }^{ 2 }\) Find the partial elasticities \(\frac { { E }q }{ { E }p_{ 1 } } \)and \(\frac { { E }q }{ { E }p_{ 2 } } \) when P₁ = P₂ = 2

Find the marginal productivities of capital (K) and labour (L) if p = 8L - 2k + 3k² - 2L² + 7KL when k = 3 and L = 1

The total cost function y for x units is given by y = 4x\(\left( \frac { x+2 }{ x+1 } \right) +6\), Prove that marginal cost decreases as x increases.

Find the equilibrium price and equilibrium quantity for the following functions. Demand: x =100 – 2p and supply: x = 3p –50

Given C(x)= \(\frac { { x }^{ 3 } }{ 6 } \)5x+200 and p(x) = 40–x are the cost price and selling price when x units of commodity are produced. Find the level of the production that maximize the profit.

If u = xy+sin(xy), show that \(\frac { \partial ^{ 2 }u }{ \partial x\partial y } =\frac { \partial ^{ 2 }u }{ \partial y\partial x } \)

Find out the elasticity of demand for the following functions
(i) p = xe^x
(ii) p = xe^-x
(iii) p = 10\({ e }^{ -\frac { x }{ 3 } }\)

For the function y=x³ +19 find the values of x when its marginal value is equal to 27.

Part - B

Generic 5 - Answer All Question

The demand for a commodity x is q= 5-2p₁+P₂ -\({ p }_{ 1 }^{ 2 }{ p }_{ 2 }\) .Find the partial elasticities \(\frac { Eq }{ { EP }_{ 1 } } \) and \(\frac { Eq }{ { EP }_{ 2 } } \) when p₁=3 and p₂=7

A firm produces x tonnes of output at a total cost of C(x) \(\frac { 1 }{ 10 } \)x³-4x²-20x+7 find the
(i) avarge cost
(ii) average variable cost
(iii) average fixed cost
(iv) marginal cost and
(v) marginal average cost.

The total revenue (TR) for commodity x is \(TR=12x+{x^2\over2}-{x^3\over 3}\)S.T. at the highest point of average revenue (AR), AR = MR
For some firm, the number of units produced when using x units of labour and y units of capital is given by f (x, y) = 80x^1/4 y^3/4. Find (i) Both marginal productivities (ii) Evaluate and interpret the results when 625 units of labour and 81 units of capital are used

A manufacturer has to supply 12,000 units of a product per year to his customer. The ordering cost (C₃) is Rs 100 per order and carrying cost is Rs 0.80 per item per month. Assuming there is no shortage cost and the replacement is instantaneous, determine the
(i) economic order quantity
(ii) time between orders
(iii) number of orders per year

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11th Business Maths Weekly Test - 2 ( Applications of Differentiation )

MABS Institution

11th Business Maths Weekly Test - 2 ( Applications of Differentiation )-Aug 2020

Part - A

Generic 2 - Answer All Question

For the demand function p = 550–3x– 6x2 where x is quantity demand and p is unit price. Show that MR = \(p\left[ 1-\frac { 1 }{ { n }_{ d } } \right] \)

A tour operator charges Rupees 136 per passenger with a discount of 40 paisa for each passenger in excess of 100. The operator requires at least 100 passengers to operate he tour. Determine the number of passenger that will maximize the amount of money the tour perator receives.

The demand for a quantity A is q=13 - 2P1 - \({ 3p }_{ 2 }^{ 2 }\) Find the partial elasticities \(\frac { { E }q }{ { E }p_{ 1 } } \)and \(\frac { { E }q }{ { E }p_{ 2 } } \) when P1 = P2 = 2

Find the marginal productivities of capital (K) and labour (L) if p = 8L - 2k + 3k2 - 2L2 + 7KL when k = 3 and L = 1

The total cost function y for x units is given by y = 4x\(\left( \frac { x+2 }{ x+1 } \right) +6\), Prove that marginal cost decreases as x increases.

Find the equilibrium price and equilibrium quantity for the following functions. Demand: x =100 – 2p and supply: x = 3p –50

Given C(x)= \(\frac { { x }^{ 3 } }{ 6 } \)5x+200 and p(x) = 40–x are the cost price and selling price when x units of commodity are produced. Find the level of the production that maximize the profit.

If u = xy+sin(xy), show that \(\frac { \partial ^{ 2 }u }{ \partial x\partial y } =\frac { \partial ^{ 2 }u }{ \partial y\partial x } \)

Find out the elasticity of demand for the following functions (i) p = xex (ii) p = xe-x (iii) p = 10\({ e }^{ -\frac { x }{ 3 } }\)

For the function y=x3 +19 find the values of x when its marginal value is equal to 27.

Part - B

Generic 5 - Answer All Question

The demand for a commodity x is q= 5-2p1+P2 -\({ p }_{ 1 }^{ 2 }{ p }_{ 2 }\) .Find the partial elasticities \(\frac { Eq }{ { EP }_{ 1 } } \) and \(\frac { Eq }{ { EP }_{ 2 } } \) when p1=3 and p2=7

A firm produces x tonnes of output at a total cost of C(x) \(\frac { 1 }{ 10 } \)x3-4x2-20x+7 find the (i) avarge cost (ii) average variable cost (iii) average fixed cost (iv) marginal cost and (v) marginal average cost.

The total revenue (TR) for commodity x is \(TR=12x+{x^2\over2}-{x^3\over 3}\)S.T. at the highest point of average revenue (AR), AR = MR

For some firm, the number of units produced when using x units of labour and y units of capital is given by f (x, y) = 80x1/4 y3/4. Find (i) Both marginal productivities (ii) Evaluate and interpret the results when 625 units of labour and 81 units of capital are used

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Tamilnadu Stateboardszs - Class

For the demand function p = 550–3x– 6x² where x is quantity demand and p is unit price. Show that MR = \(p\left[ 1-\frac { 1 }{ { n }_{ d } } \right] \)

The demand for a quantity A is q=13 - 2P₁ - \({ 3p }_{ 2 }^{ 2 }\) Find the partial elasticities \(\frac { { E }q }{ { E }p_{ 1 } } \)and \(\frac { { E }q }{ { E }p_{ 2 } } \) when P₁ = P₂ = 2

Find the marginal productivities of capital (K) and labour (L) if p = 8L - 2k + 3k² - 2L² + 7KL when k = 3 and L = 1

Find out the elasticity of demand for the following functions
(i) p = xe^x
(ii) p = xe^-x
(iii) p = 10\({ e }^{ -\frac { x }{ 3 } }\)

For the function y=x³ +19 find the values of x when its marginal value is equal to 27.

The demand for a commodity x is q= 5-2p₁+P₂ -\({ p }_{ 1 }^{ 2 }{ p }_{ 2 }\) .Find the partial elasticities \(\frac { Eq }{ { EP }_{ 1 } } \) and \(\frac { Eq }{ { EP }_{ 2 } } \) when p₁=3 and p₂=7

A firm produces x tonnes of output at a total cost of C(x) \(\frac { 1 }{ 10 } \)x³-4x²-20x+7 find the
(i) avarge cost
(ii) average variable cost
(iii) average fixed cost
(iv) marginal cost and
(v) marginal average cost.

For some firm, the number of units produced when using x units of labour and y units of capital is given by f (x, y) = 80x^1/4 y^3/4. Find (i) Both marginal productivities (ii) Evaluate and interpret the results when 625 units of labour and 81 units of capital are used