please help me with this

Question

Suppose that the revenue​ R, in​ dollars, from selling x cell​ phones, in​ hundreds, is R(x)=-1.2x^2+246x

The cost​ C, in​ dollars, from selling x cell​ phones, in​ hundreds, C(x)-0.07x^3 -2x^2+45x+450

​(a) Find the profit​ function, P(x)=R(x)−C(x).

​(b) Find the profit if x=21 hundred cell phones are sold.

​(c) Interpret ​P(21​).

Answer 1

Those equations look pretty daunting, but what the problem is asking us is not too scary. Let's do this one a time

1) P(x) = R(x) - C(x)

Well, we know R and C, we just need to subtract them and simplify the equation. So, the equation should first look something like this:

(-1.2x² + 246x) - (0.07x³ -2x²+45x+450)

Now, we simplify!

P(x) = -0.07x³ + (-1.2 + 2)x² + (246- 45)x - 450 = -0.07x³ + 0.8x² + 201x - 450

If that is a negative sign at the beginning of C(x), then it should be the same thing, but with a little extra sign:

P(x) = (-1.2x² + 246x) - (-0.07x³ -2x²+45x+450)

P(x) = +0.07x³ + 0.8x² + 201x - 450

2) Find the profit if 21 hundred cell phones are sold.

Since the equation is in hundreds, we just need to evaluate P(x) at x = 21

P(21) = -0.07(21)³ + 0.8(21)² + 201(21) - 450 = 3475.3

If 0.07x³ was negative to begin with, we then get a slightly different answer,

P(21) = 0.07(21)³ + 0.8(21)² + 201(21) - 450 = 4772.07

3) We're definitely making money at P(21) because our number is positive. A negative number would mean we're spending more money making phones than selling phones and we should find a way to fix that.