Question

My profit formula is P = -.005x^2 + 4x - 200. The question wants me to find the number of donuts sold (what they are talking about in the problem) that will generate the highest profit. How do I determine that? Thank you.

Answer 1

the highest profit to be attained is 0,making it a quadratic equation,find x,any value not x gives a loss(-P)

Answer 2

highest profit is at the vertex, when x = -b/2a = 4/.01 = 400

P(400) = 600

Answer 3

Steve,
Thank you - this makes sense that the highest profit is at the vertex, but where is the x = =b/2a from, and where is the 4/.01 = 400 from? I'm having trouble connecting those numbers.

Thanks for clarifying for me.

Answer 4

Steve is probably off line now, so I will answer.

For any quadratic function of the form
y = ax^2 + bx + c
<b>the x of the vertex is -b/(2a)</b>, once you have the x you just sub that back into the equation to get the y of the vertex.

In your case:
P = -.005x^2 + 4x - 200
a = -.005
b = 4
then x = -b/(2a) = -4/(-.010) = 4/.01 = 400

P(400) = -.005(400)^2 + 4(400) - 200 = 600

so the vertex is (400,600)

Answer 5

Thank you both!