00:01
Hello students, let us discuss the solution of this question.
00:04
Here, the price of 4k tvs is given by p and x is a number of 4k tvs and c of x is equal to total cost in dollars.
00:19
So the expression x is equal to 9 ,000 minus 30 p where x is a number of 4k tvs.
00:25
C of x, the cost is given by 1 ,050 ,000 plus 30 x.
00:30
Now, in the first of part of this question we have to calculate the price p as a function of demand and we have to find the domain of this function so let us discuss the solution of this question x is equal to 9 000 minus 30 p now 30 p is equal to 9 000 minus x so p will be equal to 9 000 minus x so p will be equal to thousand minus x whole divided by 30 p of x is equal to 9 ,000 divided by 30 is 300 minus x divided by 30 now p is always greater than or equal to zero that means price is always greater than or equal to zero therefore 300 minus x divided by 30 is greater than or equal to zero and therefore we have 9 ,000 is greater than or equal to x.
02:02
That means we have the domain of this function as x is greater than or equal to 0 and greater than or equal to 9 ,000.
02:15
Therefore, we have the price function is equal to 300 minus x divided by 30 and domain of this function is 0 is less than or equal to x is less than or equal to 9 ,000.
02:37
Let's move to the next part of this question.
02:40
In the next part of this question, it is asked to find the marginal cost function.
02:46
So let us discuss the solution of this question.
02:50
The marginal cost function is given by c prime of x.
03:03
Therefore, c of x is equal to 1 5000000 plus 30 x.
03:16
C prime of x is equal to differentiation of this which is 0 and differentiation of this which is 30.
03:28
If you add both, you are going to get 30 only.
03:31
So the marginal cost function cost function is equal to 30.
03:51
Let's move to the next part of this question...