Okay. Number 26. Number 26. We have the following information. Total cost, total revenue. We're going to figure a profit equation and then maximize it. So let's go for it. Profit equation. That is P of X. That's going to equal. They are, which is five x on We're going to subtract this whole equation here. 0.1 X squared plus 1.2 X plus 60. Okay, so we're gonna have to go ahead. Make sure we distribute this across so we can bring our light terms together minus 1.2 X minus 16. I'm gonna move this down a little bit. Yeah. Okay, so we bring our ex terms together, and we're gonna have 3.8 minus this amount minus 60. Okay, so this is our p of X equation. We can go ahead now and find the derivative of B lacks. And that's gonna be 3.8 minus 0.2 X. Linus 60. Okay, So what happens here is we have the derivative, and the derivative is, uh, corresponds to If this were the equation, right, there is some sort of spot right at the top that's the maximum happens in some X. Um, we used P prime of X, right? That's the same as the sloping zero. It's the slope. So if p private X zero we know we have a flat spot, and so we know we have the maximum. Okay, So garden. So that's equal to zero. Oh, you know what? I just did? I just have that minus 60. The end. I did not mean to do that. Bad. Bad, bad. Okay, scratch that. 0.2 x, which also will mean that negative 3.8 is equal to negative 0.2 x. Let's divide both sides by negative 0.2 Negative 0.2 and we'll come up with X equals 1900. And that is again in units, not dollars. That's an X represents. Okay, so 1900 units, so Well, let's go. Put that over here. That's half of our answer. Number of units 1900. Um, we have to find the maximum profit. So we take 1900 we put it through this equation right here. That's our profit equation. right. So we're gonna have to go ahead and take that, and we're gonna substitute in 1900 every time there's an X. So we see if I can at least get that written down before I'd defer to the calculator. Oh, actually, this is PM 1900 isn't it? P of 1900? Okay. Equals 3.8 times 1900. Minus 0.1 times 19 100. Also, those 1900 squared minus 16. So P of 1900 obviously equals 3550. Amazing. Okay, so that's gonna be our dollars. So 3550. Okay. So to reiterate, you're selling 1900 units, and then we are getting $3550 back. Thanks.