00:01
Great, so in this problem we start off with the following.
00:03
We are given p to equal to 530 minus 0 .05x and also we are given c, the cost, c of x to equal to 0 .00007x cubed minus 0 .02x squared plus 300x plus 60 ,000.
00:38
With that we start off with part a.
00:40
To find the revenue, r of x is going to be p times that's just going to be 530x minus 0 .05x squared.
00:52
We are also asked to find the profit.
00:54
Profit is equal to the revenue minus the cost.
00:58
So therefore, the profit will just be equal to negative 0 .00007x cubed minus 0 .03x squared plus 230x minus 60 ,000.
01:19
That's the profit.
01:20
For part b, we are asked to find the marginal cost.
01:25
The marginal cost c prime of x is the derivative of the cost, which in our case, the derivative of the cost, c prime will just be 0 .000021x squared minus 0 .04x plus 300...