Alright. In this problem, we have a business owner who is looking to maximize her profit and we know some information about the prices. Sheikhoun sell her product her sweatshirts for in the quantities at which she can sell. And we know some information about her revenues and costs. So how we're going to approach this is go through and for each person quantity, we're gonna find the total revenue which will be priced times quantity, to see how much money she's bringing in from sales. And then we're going to find the total costs. And it's important to note that we have two different types of costs. We have a fixed cost of $1000 per week for her Web service. Then we have a marginal cost of $20 per sweatshirt being sold. So we have to make sure we're multiplying that marginal cost by the quantity and we're always adding on that fixed cost. So here's our equation for costs here, fixed cost plus marginal cost, times quantity and then once we have those, we confined our profit simply by subtracting all of our costs from all our revenue, and that will be our economic weekly profit. So I've got no started here. This first one is a little self explanatory. You're not going to make much of a profit because you're selling at a price of zero. Um, but to go through the process, we have that price. Times quantity for revenue will be zero, and we're still incurring costs because you have that fixed costs of $1000 a week and you still have to pay $20 for each sweatshirt. And our quality of sweatshirts is 100. So, um, 100 plus another 1000 plus 2000 or costs are 3000 zero minus 3000 are profit is negative 3000. You probably wouldn't want to operate in this situation. We'll keep going to see if that increases at a price of $20 you can sell 80 sweatshirts revenue price times quantity, 1600 in our costs, we still have a $1000 fixed cost. This time we're adding on our marginal cost of 20 times. 80 is our quantity. So 1000 plus 20 times 80 is 2600 as our costs, um so our revenue 1600 minus our costs 2600 give us a profit of negative 1000. So we're still operating at a loss here. So we'll move on to the next one at a price of 40 weaken cell 60 sweatshirts. So our revenue here will be priced times quantity 40 times 60. And that is a revenue of 2400, which is looking good Better than before andare costs. We still have our fixed costs of 1000. We still are marginal cost of 20. But we're gonna multiply that 20 now by 60 and we're going to get a total cost of 2200. We at that all together. And so we have revenue of 2400 cost of 2200. Our profit is now 200. So it's good we're in. The positives were making a profit, but we'll keep going to see if we can do better at a price of 60 Weaken sell 40. Our revenue is 60 times 40. Um, and so we're gonna get the same revenue is before we multiply those. It's gonna be 2400 for a revenue. But our costs will change because their quantity is changing. So we still that $1000 fixed cost, and we have that $20 marginal cost. But we're multiplying that by just 40 this time, Um, s O that means our cost will be 1000 plus 20 times 40 which gives us 1600 and so are our profit will be 2400, minus 1600 which gives us $600 of profit. That is looking good, but we'll keep going, just in case we can do even better. Um, at a price of 80 quantity is 20. So 80 times 20 gives us a revenue of 1600 and our costs will be 1000 for fixed costs plus marginal cost 20 times the quantity of 20. Um so that gives us 1400. And so our profit is again going down to 200 and it's always good to check. Do this last one. But I'm not gonna bother. It might not be totally worth your time because the quantity is zero. So it's gonna be kind of similar to that for a situation where you're not bringing in any revenue, but you still have cost, so you know you're gonna have a negative profit here. So now that we have all of our profits. We can look at where that is highest, and we can see that it is here when we're making an economic profit of $600 per week. So that is our total weekly economic profit. And that is that this profit maximizing point. So we can now define, um, this point where the price of each sweatshirt it's is $60 and the quantity sold is 40. These are our profit maximizing price and quantity, and again, economic profit is $600.