at present, a firm is manufacturing2000 items.it is estimated that the rate of change of productionp w.r.t. additional number of workers x is given by dp/dx =100-12x.if the firm employs 25 more workers ,then the new level of production of items is
p = 2000 + 100 x - 6 x^2
if x = 25
p = 2000 + 2500 - 3750
p = 750
not a wise decision unless there is a typo
To find the new level of production of items when the firm employs 25 more workers, we need to integrate the given rate of change equation and substitute the value of x as the additional number of workers. Let's go step by step:
Given: dp/dx = 100 - 12x
We want to find the new level of production of items when the firm employs 25 more workers, so x = 25.
Integrate both sides of the equation with respect to x:
∫ dp/dx dx = ∫ (100 - 12x) dx
Integrating, we get:
p = 100x - 6x^2 + C
Where C is the constant of integration.
Now, substitute the value of x as 25:
p = 100(25) - 6(25)^2 + C
= 2500 - 6(625) + C
= 2500 - 3750 + C
= -1250 + C
The new level of production of items when the firm employs 25 more workers will be -1250 + C.