SOLUTION: [ The profit that a company makes depends on the price, p, that they sell their items. The company's profit is determined by f(p) = -2p^2 +24p -54 thousand dollars. At what price

Question 819463: [ The profit that a company makes depends on the price, p, that they sell their items. The company's profit is determined by f(p) = -2p^2 +24p -54 thousand dollars. At what price (to the nearest cent) should the company price their items to earn a profit of $15,000? ]
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
f(p) = -2p^2 + 24p - 54
15 = -2p^2 + 24p - 54
-2p^2 + 24p - 69 = 0
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the above quadratic equation is in standard form, with a=-2, b=24, and c=-69
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to solve the quadratic equation, by using the quadratic formula, plug this:
-2 24 -69
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
p = 4.77525513
p = 7.22474487
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answer:
the company may price its items at either of these prices:
$4.78
$7.25
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php
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