# Find Equilibrium quantity and price.

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The quantity of watches demanded per month is related to the unit price by the equation:

p = d(x) = 50/ (0.01x^2 + 1) (1 less than equal x less than equal 20)

where p is measured in dollars and x is measured in units of a thousand. The supplier is willing to make x thousand watches available per month when the price is given by p =s(x) = 0.1x + 20 dollars.

Find the equilibrium quantity and price.

https://brainmass.com/math/calculus-and-analysis/finding-equilibrium-quantity-price-351371

#### Solution Preview

At equilibrium, demand = supply

50/(0.01x^2 + 1) = 0.1x + 20

50 = (0.01x^2 + 1)(0.1x + 20) = 0.001x^3 + 0.20x^2 + 0.1x + 20

0.001x^3 + 0.20x^2 + 0.1x - 30 = 0

We solve for x using Newton-Raphson Method

f(x) = 0.001x^3 + ...

#### Solution Summary

This solution shows all the steps for calculating the equilibrium quantity and price in the given problem.

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