The TechStuffs company has determined that the function P(q)= -14+101.4x-3x^2 represents the profit

Question

The TechStuffs company has determined that the function
P(q)= −14+101.4x−3x^2 represents the profit from selling x thousand TouchTips touchpads. How many touchpads should be sold, in order to maximize the company's profit?

Answer 1

Hi Kelani,

 

Our function is 

P(q) = -14 + 101.4x - 3x²

I believe it should either be P(x) or the x's should be q's.

 

I'm going to rewrite this equation, rearranging the terms on the right side.

 

P(x) = -3x² +101.4x - 14

 

If we were to graph this function, we would have a parabola, downward facing.

Profits are maximized at the top of the parabola, i.e. at the vertex.

 

The number of touchpads which maximizes the profit is found by determining the x coordinate of that vertex.

 

This is found using the expression -b/2a, where a and b are defined from the general equation of a parabola:

f(x) = as²+bx+c

 

In the profit formula given, a = -3 and b = 101.4

 

-b/2a = -101.4/[(2)(-3)] = -101.4/-6 = 16.9

 

Remember this is in thousands.

 

So profit is maximized when at 16.9*1000 touchpads = 16,900