Question

A company that sells digital cameras has found their revenue can be modeled by the equation R(p)=-5p^2+1230p where p is the price of the camera in dollars.

What price will maximize their revenue?

What is the maximum revenue?

(no need to include units, just the number. )

Answer 1

To determine the price that will maximize the company’s revenue, we need to find the value of p that corresponds to the top of the revenue function R(p) = -5p 2 + 1230p.

The general form of this function is a parabola directed downwards, which means that the top of the parabola will correspond to the price that maximizes revenues. The corresponding price can be found using the following formula: p = -b/ (2a),

In equation R(p) = -5p 2 + 1230p, we can see that a = -5 and b = 1230. By substituting these values in the formula, we have:

p = -1230 / (2 * -5)

p = -1230 / -10

p = 123

The price that will maximize the company’s revenue is 123.

pour trouver le revenu maximum, nous pouvons substituer cette valeur de p dans l'équation de revenu R(p) :

R(123) = -5 * 123^2 + 1230 * 123

R(123) = -5 * 15129 + 151230

R(123) = -75645 + 151230

R(123) = 75585

Le revenu maximum de l'entreprise sera de 75 585

Explanation: