Hello. This poem is five parts to it, a B city. What we are given is that the company has a cost functional. C off Q equals 4000 plus two Q dollars on dhe. Its revenue function is are cute. Use 10 Q dollars. Q. Is the quantity produced for costing? Forever New is the quantity. So, uh, okay, wish you a the question of fixed cox fixed costs, fixed costs. We look at the way we look at the and of course function. Uh, has two turns. The 1st 3rd does not have any Q involved here and the second term has queuing. Also, this term will give us the variable cost times the number off units produced. So we put if cube equals zero. That means we haven't produced any. Uh, I think is you. The cost of producing zero items will be two times 00 plus 4000 4000. So the answer to question a fixed costs are $1000. Okay. Questioning marginal coast marginal costs. Murder because him c equals marginal cost equals the derivative off the cost function by the variable. Here, uh, it's years are unit off. See, which is doors. Two units. Oh, Q On the meaning of the marginal cost is how much both cost increase when we increase the the unit production by one, which is in fact here. This is only near a function this is going to be soon We consider is going to be too, because this is a slope off the graph of doing your function. But let us do the let us do the differentiation first. Emcees sorry. Him sees a function of here. So it is the derivative seen by the words you, which is the derivative of the first times zero. Because this costume ah, the riveted off two times skewed is too. To what? It's $2 additional growth. The, you know called, huh? Conditional. Michael produced. Okay. Uh, question C, He's extract from the revenue functional on. Did ask what is the price, huh? Okay, Now we in general, not in general. But the revenue function is defined as the price, per I think times the number about him. So So what do we see here? We see that this can only be big. Friend said price is be easy. Thing on The answer is 10 Gore's her Okay. What should the we need to Graff? Okay, I need some preparation. All think Paul's okay? Let's, uh, drew the horizontal axis on which we will place quantity on. We're going to be graphing. We're going to grab, see if Q on DDE C, Q on and the are here. The same access. So we get the door amount here, and this will be a quantity. Okay, Breath arc, you will be easier. Are you? Let's find some for zero quantity. The art is going to be zero. So this will be on the graph of our on dhe with C that we take one of these to be 102 34 Let's say this is 100 500 678 9000 units. And so, um, 500 units, 10 times 100 with lee, five thousands. So let's place this to be 1000 to 34 Let's put this to be 5000 which makes this one thousands. And the points of the graph of the revenue is 500,000 and revenue over is linear and fastest through these two points. So this would be revenue. Ah, the costs ocean. The cost function is a linear function. And the sorry when cute zero we're cost is for thousands. So we have seen tricep, uh, vertical lists of all 4000 witches here on Let's take 500 here as well. When the quantity is 500 then we have two times 500,000 plus 4000 is 5000 which comes in handy because we are we then no. But a certain breaking point is going to be here. So this is the cost off. They want to give the point. Here off intersection is five hundred's by thousands. And this will be our zero, where the break even point is the point where the cost of Q equals the revenue off you. Let's see, what is the cost of producing Crime 100 units? It is what doesn't and what is the revenue Looking at the black breath revenue again? This point he's 5000 equals revenue 5000. Okay, now, if we have a look at what happens with profit, the prophet function is the function, the difference between the revenue and the cost. It's going to be positive when revenue is greater than the cost. When the graph off the revenue is above. Let's hear the two breaths are, uh, the same points so we could say our is equal to you here. And this is the point where the rocket is made. He is Pines equals zero again in this part of the graph, when cues greater than 500 in this part of the grand, the revenue function is above the cost function. So this is where the profits will be possible. Hear from 0 to 500 quantity, we have the cost being above the cost being above the revenue. So we are subtracting greater number from a smaller number, which results in the profit being negative. And that's one of the questions. How do we know that when the once he produced is greater than the breaking point that the company will make a profit? The reason is because in the areas for, uh, Hugh greater than here zero, which is we can't be certain, but we can't, uh, until we actually calculated. But for the time being, we're taking the Q zero. That is the breaking point is 500. Uh, the revenue is greater than the cost, so profit is positive. What does it mean basil? The company is making money before the five country profits Negative. It means that the company's making off. Finally, Part B is to calculate when he's the revenue function equal the cost function. Uh, we heat the week. The breaking point here By chance, we found 500 to yield arrive in your 5000 and also 500 to yield 5000. But should we have chosen that, say, where a quantity of 1000? We would have gotten two different points and it wouldn't have been so obvious Where this breaking point? What's So we do this outbreak Lee we saw what is Q zero p zero will be the solution to the equation where revenue equals cost. Okay, so what is the function of revenue? The revenue is 10 Q. And that should equal thing here should equal 4000 plus 4000 plus to you. Subtract took you from either side. We have eight year that equals 4000 and divided by eight. Hugh equals 500 which confirms our graphical biographical solution, and this souls befo the whole train. Okay. Ah, wanted the people's 500 is just one more thing What is the revenue cost? So are 500 equals. We calculate that here equals $5000. Hm. Hey, we have So be so. See the Andy. We have the whole problem, so I hope it helps.