Answer:
Step-by-step explanation:
Given
Production is given by
[tex]P=5000\left [ 1-\frac{4}{4+e^{-0.002x}}\right ][/tex]
(a)when [tex]x=100[/tex]
[tex]P=5000\left [ 1-\frac{4}{4+e^{-0.002\times 100}}\right ][/tex]
[tex]P=5000\left [ 1-\frac{4}{4+e^{-0.2}}\right ][/tex]
[tex]P=849.53\ units[/tex]
(b)When [tex]x=500\ units[/tex]
[tex]P=5000\left [ 1-\frac{4}{4+e^{-0.002\times 500}}\right ][/tex]
[tex]P=5000\left [ 1-\frac{4}{4+e^{-1}}\right ][/tex]
[tex]P=413[/tex]
(c)When there is no limit in x i.e. x tends to [tex]\infty[/tex]
[tex]P=5000\left [ 1-\frac{4}{4+e^{-\infty }}\right ][/tex]
[tex]P=5000(1-1)=0[/tex]
as x increases value of P is decreasing
