Home
Class 12
MATHS
At present, a firm is manufacturing 2000...

At present, a firm is manufacturing 2000 itmes. It is estimated that the rate of change of production P w.r.t. additional number of workers `x` is given by `(dP)/(dx)=100-12sqrt(x)`. If the firm employs 25 more workers, then the new level of production of items is

A

(a) 2500

B

(b) 3000

C

(c) 3500

D

(d) 4500

Text Solution

Verified by Experts

The correct Answer is:
(c)
Given, `(dP)/dx=(100-12sqrtx) rArr dP=(100-12sqrtx)dx`
On integrating both sides, we get
`int dP=int (100-12sqrtx)dx`
`P=100x-8x^(3//2)+C`
When `x=0, then P=2000 rArr C=2000`
Now, when x=25, then is
`P=100xx25-8xx(25)^(3//1) +2000`
`=2500-8xx125+2000`
=4500-1000+3500
Promotional Banner

Similar Questions

Explore conceptually related problems

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by (d P)/(dx)=100-12sqrt(xdot) If the firm employs 25 more workers, then the new level of production of items is (1) 3000 (2) 3500 (3) 4500 (4) 2500

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005x^(3)- 0.02 x^(2)+30x+5000 Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 3x^(2) + 36x + 5. Find the marginal revenue, when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant.