Question

Demand the demand function for a product is modeled by

Answer 1

Answer:

Step-by-step explanation:

Given

Production is given by

$P=5000\left [ 1-\frac{4}{4+e^{-0.002x}}\right ]$

(a)when $x=100$

$P=5000\left [ 1-\frac{4}{4+e^{-0.002\times 100}}\right ]$

$P=5000\left [ 1-\frac{4}{4+e^{-0.2}}\right ]$

$P=849.53\ units$

(b)When $x=500\ units$

$P=5000\left [ 1-\frac{4}{4+e^{-0.002\times 500}}\right ]$

$P=5000\left [ 1-\frac{4}{4+e^{-1}}\right ]$

$P=413$

(c)When there is no limit in x i.e. x tends to $\infty$

$P=5000\left [ 1-\frac{4}{4+e^{-\infty }}\right ]$

$P=5000(1-1)=0$

as x increases value of P is decreasing