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 equals negative 0.5 x squared plus 36 x minus 179 models the profit of the fundraiser.​ What's the smallest​ amount, in​ dollars, that you can charge and make a profit of at least ​$379​?

To make the desired​ profit, the smallest amount you can charge for each box is ​$
nothing.

Answer 1

We need to charge $22.58 to have $379 profit.

Explanation:

The given equation is:

`p=-0.5x^(2)+36x-179`

Where x is the amount the class charges.

So, the problem is asking the smallest amount that can be charged if the profit is $379. Replacing this data, the expression would be:

`-0.5x^(2)+36x-179\geq 379`

"at least" means "equal or more than".

Now, we have to solve this quadratic inequality, which we can do by just graphing, because the solution of inequalities are intervals, which are specific regions.

As you can see in the image attached, the smallest amount is

`x=-6√(5)+36=22.58`

Therefore, we need to charge $22.58 to have $379 profit.

Answer 2

$ 22.6

Explanation:

Given that

Price charged for each box of seeds = x

Profit gained from from selling boxes of seeds = p

The equation of profit is modeled as

P(x) = 0.5x² + 36x - 179

As per given information if the fundraisers make a profit of $379 then find the minimum price charged for each box of seed.

Now our above equation becomes

379 = -0.5x² + 36x - 179

Simplifying

379+179 = -0.5x² + 36x

558 = -0.5x² + 36x

0.5x² - 36x + 558 =0

multipying both sides of equation by 2

2(0.5x² - 36x + 558) = 2x0

x² - 72x +1116 = 0

Using quadratic formula we get the following factors

x= 49.4 or x= 22.60

As we can the smalles value is 22.6

So, they can charge 22.6 dollar for each bag of seeds in order to get profit of 379 dollars.