00:01
Hello, so here we have our function r of p, what is it going to be equal to negative 4p squared plus 4 ,000 p.
00:12
We want to know what unit here price p maximizes revenue.
00:15
Well, the max or min is going to occur at the vertex.
00:18
So we have the a value is negative.
00:19
I mean, the parabola here is going down.
00:22
So if it goes down, we do have a maximum value to define the maximum.
00:26
Define the vertex, we can go ahead and put this in the vertex form.
00:28
That's the form a times the quantity x minus h quantity squared plus k if it's in that form then the vertex is at the point h comma k so to do so we want to first we want me to have the a value the coefficient on x squared has to be one is right now it's negative four we could factor out the negative four and we have negative four times the quantity we have p squared and then negative uh uh so negative four times um negative um negative um negative um thousand is going to be 4 ,000 p, so negative 4 p squared and then minus 1 ,000 p.
01:07
Then taking half of the coefficient, now on a linear term, so half of negative 1 ,000 is going to be negative 500, and then 500 squared, or 500 times 500 is going to be 200 and 50 ,000.
01:22
So we take plus 200 ,000, is going to be equal to, well, zero...