PLEase help me with this math problem....?

Question

Find the number of computer units x that needs to be sold to produce a maximum profit P (in pesos) if P (x) = 900 x - 0.1x^2

Could you please help me with this problem and please put your solution or an explanation on how did you get the answer

Thanks ^_^

Answer 1

Notice that the equation you show is a parabola. Also notice that it is an upside down parabola (b/c of the negative infront of the 0.1). It's like an unhappy smile, so the tip of it is the maximum.

Remember how since it's a quadratic equation it has the form of
f(x)= ax^2 + bx + c

If we rearrange yours it would be,
P(x)= -0.1x^2 + 900x + 0

Now to get to the maximum/minimum, you need to get the vertex of the equation, the formula for those coordinates would be,

{-b/(2a) , f( -b/(2a)) }

= ( -900/ (2*-0.1), P( -900/ (2*-0.1) )
= ( 4500, P(4500) )
= ( 4500 , 2025000 )

so the max # of profits needed to sold would be 4500 to get a profit of 2025000.

Answer 2

the parabola in this problem opens downward. This is because the coefficient of the x^2 term is -.1

And the maximum profit is when the parabola has reached it's vertex.

The vertex is at (4500, 2,025,000).

To get the vertex, use (-b/2a,f[-b/2a]). The -b/2a is -900/(2(-.1)) which equals 4500. Then plug this number into the original problem and that equals 2,025,000.

So the maximum profit is 2,025,000. This occurs when 4500 computer units are sold.

Answer 3

To find Pmax(x), we need to find the value of x where the derivative of P(x) is 0. Check out your derivative question - it directly applies to this one...

P(x) = 900x -0.1x^2 (or 900*x^1 - 0.1*x^2)
P'(x) = 1*900*x^0 - 2*0.1*x^1
P'(x) = 900 - 0.2*x

For what x is P(x) = 0?

900 - 0.2*x = 0
-0.2*x = -900
x = 4500

If you want, you can test this by checking 4400, 4500 and 4600 in the original P(x).

Answer 4

I don't understand your equation - is that 900 times negative zero point 1 divided by 2? Or is that 900(x) minus zero point one divided by 2?
That's important information.
Just to be silly, considering that it is about 11 pesos to equal one American dollar, you would need to sell one computer at 9000 pesos to get the value of about 900 American dollars. To make a profit, you would have to factor in the lowest selling price of the computer, say 300 dollars, plus 40 percent markup, (120 dollars), minus cost of shipping and handling (say 20 bucks) and cost of assistant you hired to help with daily taks of handling, packaging, and going for your daily Starbucks coffee (that's nine bucks an hour for eight hours a day for your employee, you gotta pay yourself at least 10 bucks an hour for your work, plus seventy five bucks a day for daily expenses ($375 a week, it covers your daily Starbucks run and lunches), so you have to clear at least $1135 a week. If you sell at least 1 computers at day at a total cost of $440 per unit for 5 days for a total $2200 a week you would make a profit of $1065 a week. To break even you would have to sell at least 2 computers a week. I am not even going to convert it into pesos, because everyone knows nobody in Mexico uses pesos any more, except for the Guatemalans working in Mexico who get paid in Pesos. (Don't get mad at me for pointing that out, it's the truth and they know it.)
That's not your formula, I know, but it is what happens in real life. Just a heads up for real life in the future minus homework and theoretical math formulas that work on paper and go all to pieces in reality.
P.S. Everyone vote for that other guy's answer - I'm okay with it. ;)!