00:01
Hi there.
00:02
So for this problem we need to calculate.
00:06
First, the demand function and we are given two points.
00:14
That 1 ,200 tablets computers are sell by $350.
00:29
And also that if we sell an additional of 80 tablets, so this will be this.
00:43
We can sell that for $10 less, so that will be $340.
00:54
So this is the given information, and we need to find the demand function.
01:11
We will set that p is the price.
01:15
And q is the number of tablets sold so that the function of price should be something like this, where m is the slope of this function and p0 corresponds to a given point and q -0 to another given point for the number of top of that sold.
01:57
So to find first the slope, we know that that is the change in price over the change in the number of top left sold.
02:15
So we can see in here that we put the final price minus the initial price over the final number minus the initial number.
02:27
So the final price or the second point in here is given by this because the p component or the price is greater that, so that will be the final price.
02:49
Oh no, sorry.
02:50
This is the price.
02:56
This is the price.
02:58
This is the initial.
03:02
Number of tablets.
03:06
This is the final one.
03:09
This is the initial price, and this is the final price.
03:15
So with that set, we just simply substitute those.
03:20
So it will be 340 minus 350 over all.
03:34
So this will give us minus 1 over 8.
03:41
And this is the slope.
03:44
So we just substitute this slope in this equation.
03:49
And we put some values for p0 and q2 0.
03:56
I'm going to use this point in here.
04:00
So we will have p minus p0, which is 300.
04:08
Thread and 50 is equal to the slope times q minus 1 ,200.
04:28
So solving for p, we will have that the function is 1 over 8, q plus 500.
04:42
And this is the demand function.
04:48
Now, for par b of this problem is what should the price be set in order to maximize the revenue? so in this case, we need to find the revenue function, the divided, find the maximum, and then substitute that value in the price price function.
05:17
That's what we need to do for par b.
05:20
The revenue function that we're called arc of q is the price function or the demand function times the number of tablets sold so that if we multiply that function by q, we will have 1 over 8, q squared plus 500 q.
05:50
And to find a critical point, we don't know if it is a minimum or a maximum, but to find a critical point, we derivate this function with respect to q.
06:05
So we will have 1 over 4q plus 500.
06:13
And to find a critical point, we set this to 0...