00:01
In this problem, we are provided that the demand function equals to q equals to 86 plus 0 .007 p squared and we are asked to find the quantity q when the price p equals to $480.
00:28
Dollars.
00:31
Here the price is for each board.
00:37
So now in order to find out the quantity, let us substitute the value of p as 480 in the above expression of q.
00:47
So we get q equals to 86 plus 0 .007 times 480 the whole square.
00:58
Simplifying this, we have 86 plus 0 .007 .7.
01:03
Times 230 ,400.
01:11
So now further simplifying it, we get 86 plus 1612 .8.
01:17
Adding this up we have 1698 .8 which is approximately equal to 169 units of boats.
01:30
So this is the quantity that will be sold if the price is $480 per board.
01:37
Now moving towards subpart b.
01:41
In subpart b, we are given the same demand function q equals to 86 plus 0 .007 p squared.
01:50
And here we are asked to calculate the revenue.
01:57
We know that the revenue function are equals to the demand function times the unit price.
02:05
So since we need to find out the revenue when p equals to $480, we find out the revenue by substituting q when it is equal, when p is equal to 480 and we multiplied with p which is 480...