00:01
Given revenue and cost function, we want to find the profit function and we want to see what the maximum profit is going to be.
00:07
So what we need to do first of all is know that profit is going to be your revenue minus your cost.
00:13
So we're going to take our revenue function, which is at 5900 q minus 100 q squared, and we're going to subtract the cost function, which is 2 q cubed, minus 4 q squared plus 140 q plus 845 i have to be careful that i don't misread my cues as zeros so put that in parentheses to distribute correctly so that'll be minus 2 q cubed plus 4 q squared minus 140 cube minus 845 let's get this in descending order so i'm going to have negative 2 q cubed.
00:55
It takes care of that.
00:56
Then my q squared, so i'm going to have minus 96.
01:00
Then my q's, i'm going to have plus 5 -760 q and then minus 845.
01:11
So there's my my profit function in terms of q.
01:19
Excuse me.
01:21
Next we need to maximize this, so we need to take the derivative.
01:24
So i'm going to say p -prime.
01:25
Of q is going to equal to negative 6 q squared minus that's going to be um 192 q and then we're going to have plus 5760 to maximize that we need to set it equal to zero so i'm going to look and see here that all of these are divisible by six so i'm going to divide everything by negative six so i have it easier numbers to work with so that's going to be q squared and that's going to be plus.
01:58
Let's see what 192 divided by 6 is.
02:02
32, q, and then we're going to have minus 960, and that equals to zero.
02:13
So let's think about what's going to equal.
02:15
This is going to factor.
02:16
It's just going to take a minute to figure out how it's going to factor.
02:19
So let me think here, q and q.
02:22
So 960, i know that that is going to be 10 times 96, so that's not 32...