Answer:
The answer is "1798".
Explanation:
[tex]\to p=180x-\frac{x^{2}}{1000}-2000[/tex]
In order to find the rate of profit increase each day, we differentiate between the money demand function and the time t.
[tex]\to \frac{dp}{dt}=180\frac{dx}{dt}-\frac{2x}{1000}\frac{dx}{dt} \\\\\to \frac{dp}{dt}=\frac{dx}{dt}\left (180-\frac{2x}{1000} \right ).................(1)[/tex]
Calculate [tex]\frac{dp}{dt}[/tex] when [tex]x=100[/tex]
[tex]\frac{dx}{dt}=10[/tex] (Extension rate of produced and delivered units per day)
[tex]x=100 \ and\ \frac{dx}{dt}=10 ......... in \ \ eq(1)\\\\\frac{dp}{dt} = 10\left (180-\frac{2(100)}{1000} \right )\\\\[/tex]
[tex]=10\left (180-0.2\right ) \\\\=1798 \\\\[/tex]
