Question

A small company that manufactures snowboards uses the relation P=162x-81x^2 to model its profit. In this model, x represents the number of snowboards in thousands, and p represents the profit in thousands of dollars. How many snowboards must be produced for the company to break even?

Answer 1

From the quadratic equation, it is found that the 2000 snowboards must be produced for the company to break even.

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The profit of producing x thousand snowboards is given by:

$P(x) = 162x - 81x^2$

The break even point is the value of x for which P(x) = 0, thus:

$162x - 81x^2 = 0$

$81x^2 - 162x = 0$

$81x(x - 2) = 0$

That has two solutions:

$81x = 0 \rightarrow x = 0$

$x - 2 = 0 \rightarrow x = 2$

x is in thousands, and we want the non-zero solution, thus 2000 snowboards must be produced for the company to break even.

A similar problem is given at brainly.com/question/24716530