Question

Your class is selling boxes of flower seeds as a fundraiser. The total profit p depends on the amount x that your class charges for each box of seeds. The equation p= -0.5x2 + 36x - 231 models the profit of the fundraiser. What's the smallest amount, in dollars, that you can charge and make a profit of at least $363?​

Answer 1

Answer:

The least amount is $75.50

Step-by-step explanation:

Given

$p \to profit$

$x \to amount$

$p = -0.5x^2 + 36x - 231$

Required

The smallest amount to make at least 363

We have:

$p = -0.5x^2 + 36x - 231$

Rewrite as:

$-0.5x^2 + 36x - 231=p$

Substitute 363 for p

$-0.5x^2 + 36x - 231 = 363$

Collect like terms

$-0.5x^2 + 36x - 231 + 363 = 0$

$-0.5x^2 + 36x + 132 = 0$

Using quadratic formula, we have:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where:

$a = -0.5; b= 36; c = 132$

So, we have:

$x = \frac{-36 \± \sqrt{36^2 - 4*-0.5*132}}{2*-0.5}$

$x = \frac{-36 \± \sqrt{1560}}{-1}$

$x = \frac{-36 \± 39.50}{-1}$

Split

$x = \frac{-36 + 39.50}{-1}; x = \frac{-36 - 39.50}{-1}$

$x = \frac{3.50}{-1}; x = \frac{-75.50}{-1}$

$x = 75.50$ and $x = -3.50$

The amount can't be negative.

So:

$x = 75.50$

Hence, the least amount is $75.50