Question

Your class is selling boxes of flowers as a fundraiser. The profit p depends on the amount x that your class charges for each box of seeds. The equation p=-0.5^2+36x-169 models the profit of the fundraiser. What is the smallest amount in dollars that you can charge and make a profit of $389?

Answer 1

$ 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.

NOTE.- just substitute values and resolve