4.Arestaurant uses the ratio method of pricing: It has annual nonfood costs of S800,000 and desires a profit of $150,000.Last year the restaurant spent S400,000 on ...

A catering company estimates that, if it has $x$ customers in a typical week, its expenses will be approximately $C(x)=550 x+6500$ dollars, and its revenue will be approximately $R(x)=1200 x$ dollars. (a) How much profit will the company earn in 1 week when it has 12 customers? (b) How much profit is the company making each week if the weekly costs are running at a level of $$\$ 14,750$$ ?

Let's talk about question. About 26 were given the cost off a catering company, uh, the expenses off a catering company, which are Lieutenant C X as 5 50 x plus six five double zero. Well, it's revenue is 1200 x dollars x are the number off customers. In a typical week, Party asks about the prophet look, of which the company will on and one week if it has 12 customers. So first of all, the profit has given by a revenue minus cost or revenue is 1200 x minus. If we do the cost and the cost of hers would be 1200 X minus 5 50 x plus 6500 eso. This comes out as 6 50 eggs minus 65 double zero. But we're already given that the number of customers are, uh, well. So for 12 we substitute X as well. So we get the final valuers 1300. So this is the profit and part B. It says that it z weekly cost are given, so let's right that we already know the cost function on the weekly cost will substitution that. So that is 14750 This is the weekly cost. It has given us 5 50 x like 650 So from here, if it's attracted 6500 both sides, we have 14750 minus 65 Double zero is 5. 50 x. So from here, the value of X By dividing by 5. 50 both sides, it is 14750 minus 65 double 0/5. 15. So the value of X from here comes out us. You are, uh, no. Off these customers, we need to find a profit on. We already have the equation off profit, which is 6. 50 x minus 6500. So the prophet will be 6. 50 eggs that excess 15 minus 6000 500. So this comes out us three to 50 dollars. So this is the profit

All right. So the cost function a restaurant is given by sea X y equals one forest X squared plus for ex plus two I squared. Plus why? Plus 10. Okay. And we want to find the okay. So X is the cost of labor. Why is the cost per dish? And we want to find the average cost per hour on this interval. So costs per hour ranging between 30 and 60. Mm. Cost per dish ranging between 15. 80. Okay, so we need to divide by the area of the region we're integrating over, which is just this rectangle. So 30 by 30 squares, that's nine 100 that will divide by so one over 900. And then we'll integrate secret up to 60. Integrated zero. Yeah, 30 to 60. There you go. And then 50 to 80 and we have 1/4 squared. Plus four x plus two. I squared, plus y plus 10, the y the X. All right, warned over 900. Okay, so we need an anti derivative with respect to why. So I'll be 1/4 x squared y plus four x y plus two thirds. Why cubed plus one half y squared plus 10. Bye. Evaluated from 50 to aiding. All right, so let's go over here. So we have one over 900? No. And then in your girl, 30 to 60. Mm. Okay. One for us. So these wise will all just get a factor of 30. Said that will be 30 over four x squared, and then we'll have 30. Everyone 20 x. Yes. Okay, two thirds yq. So why cute? We're going to do. Let's see. 80 cubed. Minus 50 cubed. So that is any cube minus 30. Cute. Mhm. Mhm. Okay, so 387,000. And then all times two thirds. 258,000. Okay. And then one half of okay, y squared. So they got to do 80 squared, minus 50 squared and then divided by two. Okay, 1950. And then plus 300. Okay, anti derivative time. One over 900. This is going to be 10/4 X cubed plus 60 x squared plus 258,000 us. Uh, sorry. 210,000 x was, and we can actually just add all these together might be best for now. So 258 1000 plus 1950 was 300 is 260,000. 250 x evaluated from 30 to 60. So this one is going to be easy. We're just gonna multiply this one by 30. So that's seven 807 500. Yeah. Okay. Stood on this one over 900. Right. We need to do 60 cubed, minus 30 kids, times 10 over four, 472 1005 100. And then we needed to six a C 60 squared, minus 30. Squared, right times 60. That's 100 62,000. Okay, so it had these up work. 200 seven 807 100. Okay. Got 8,442,000, and then we'll divide by the area 900. So we get the average cost. 9000 $380. Oh,

Okay, then we have advertised in a newspaper that's two by four cost $36.75. And that's based on the size of the ad that says you want. So double the length and with sir going from two by 4 to 4 by eight. Okay, so if we just find the area of these two shapes, this area would be eight, plus the units on this inches so eight square inches for $36.75. And this new, its new ad would have an area of four by eight, just 32 square inches, so we can see that the area is four times as much now. And since the cost is based on the size are new costs would be $36.75 times four, he says, four times as big costs four times as much. And that's gonna work out to $147. Even make sure you answer the whole question. Yeah, that's it. So his new advertisement, if he doubles all the sides before times as much as the original or $147 There you go

Here we have the equation in equals selling price minus cost. So we do selling, which is 2231.81 minus 16 53.19 in ruinous attract. So that gives me seven 11. Minus nine is to someone's with six 11 minus three. It's eight 12 oneness by yes, seven and then, so the answer is 178 point 62.