Question

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 dp/dx = 100 – 12√x if the firm employs 25 more workers, then the new level of production of items is

Answer 1

Given:

Current production of the firm = 2000

The rate of change of production when additional number of workers are appointed = $\frac{dp}{dx} = 100 - 12\sqrt{x}$

To find:

The new level of production.

Solution:

$\frac{dp}{dx} = 100 - 12\sqrt{x}$

Integrating both the sides w.r.t x we get:

$p = 100x - \frac{12*2x^{3/2} }{3}$ + p₀

p₀ is the initial production of the items in the firm.

p = 2500 - 1000 + p₀

p = 1500 + 2000

p = 3500

Therefore the new level of production of items is 3500.