Advertisements
Advertisements
Question
A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price per item is given as p = 120 – x. Find the value of x for which profit is increasing
Solution: Total cost C = 40 + 2x and Price p = 120 − x
Profit π = R – C
∴ π = `square`
Differentiating w.r.t. x,
`("d"pi)/("d"x)` = `square`
Since Profit is increasing,
`("d"pi)/("d"x)` > 0
∴ Profit is increasing for `square`
Advertisements
Solution
Total cost C = 40 + 2x and Price p = 120 − x
Profit π = R – C
∴ π = 120x – x2 – (40 + 2x)
= 120x – x2 – 40 – 2x
= – x2 + 118x – 40
Differentiating w.r.t. x,
`("d"pi)/("d"x)` = – 2x + 118
Since Profit is increasing,
`("d"pi)/("d"x)` > 0
∴ – 2x + 118 > 0
∴ 2x < 118
∴x < 59
∴ Profit is increasing for x < 59.
RELATED QUESTIONS
Find the marginal revenue if the average revenue is 45 and elasticity of demand is 5.
Find the elasticity of demand, if the marginal revenue is 50 and price is Rs 75.
The demand function of a commodity at price P is given as, D = `40 - "5P"/8`. Check whether it is increasing or decreasing function.
The total cost function for production of x articles is given as C = 100 + 600x – 3x2 . Find the values of x for which total cost is decreasing.
The manufacturing company produces x items at the total cost of ₹ 180 + 4x. The demand function for this product is P = (240 – x). Find x for which revenue is increasing
Find the price, if the marginal revenue is 28 and elasticity of demand is 3.
If the demand function is D = `((p + 6)/(p − 3))`, find the elasticity of demand at p = 4.
A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which revenue is increasing.
A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which profit is increasing.
A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which also find an elasticity of demand for price 80.
Find MPC, MPS, APC and APS, if the expenditure Ec of a person with income I is given as Ec = (0.0003) I2 + (0.075) I ; When I = 1000.
Fill in the blank:
A road of 108 m length is bent to form a rectangle. If the area of the rectangle is maximum, then its dimensions are _______.
If the elasticity of demand η = 1, then demand is ______.
If 0 < η < 1, then the demand is ______.
State whether the following statement is True or False:
If the marginal revenue is 50 and the price is ₹ 75, then elasticity of demand is 4
A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price per item is given as p = 120 – x. Find the value of x for which revenue is increasing
Solution: Total cost C = 40 + 2x and Price p = 120 – x
Revenue R = `square`
Differentiating w.r.t. x,
∴ `("dR")/("d"x) = square`
Since Revenue is increasing,
∴ `("dR")/("d"x)` > 0
∴ Revenue is increasing for `square`
Complete the following activity to find MPC, MPS, APC and APS, if the expenditure Ec of a person with income I is given as:
Ec = (0.0003)I2 + (0.075)I2
when I = 1000
If f(x) = x3 – 3x2 + 3x – 100, x ∈ R then f"(x) is ______.
In a factory, for production of Q articles, standing charges are ₹500, labour charges are ₹700 and processing charges are 50Q. The price of an article is 1700 - 3Q. Complete the following activity to find the values of Q for which the profit is increasing.
Solution: Let C be the cost of production of Q articles.
Then C = standing charges + labour charges + processing charges
∴ C = `square`
Revenue R = P·Q = (1700 - 3Q)Q = 1700Q- 3Q2
Profit `pi = R - C = square`
Differentiating w.r.t. Q, we get
`(dpi)/(dQ) = square`
If profit is increasing , then `(dpi)/(dQ) >0`
∴ `Q < square`
Hence, profit is increasing for `Q < square`
