Question

The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 10 + 0.002p3 and that its demand function is D(p) = 50 - 0.04p2, where p is the price. Determine the price for which the supply equals the demand.

Answer 1

$21.86 is the answer that your looking for

Answer 2

Answer: At $21.85, the supply will equal to demand.

Step-by-step explanation:

Since we have given that

Demand function is given by

$D(p) = 50 - 0.04p^2, \text{where p is the price.}$

Supply function is given by

$S(p) = 10 + 0.002p^3$

According to question, we need to find the price for which the supply equals the demand, i.e. Equilibrium price and quantity.

$D(p)=S(p)\\\\50-0.04p^2=10+0.002p^3\\\\50-10=0.002p^3+0.04p^2\\\\40=\frac{2}{1000}p^3+\frac{4}{100}p^2\\\\40=\frac{2}{100}p^2(\frac{1}{10}p+2)\\\\\frac{40\times 100}{2}=p^2(\frac{1p+20}{2})\\\\\mathrm{The\:Newton-Raphson\:method\:uses\:an\:iterative\:process\:to\:approach\:one\:root\:of\:a\:function}\\\\p\approx \:21.85861\dots$

So, at $21.85, the supply will equal to demand.