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If a company has totalcosts C(x)= 14,000 + 15x + 0.2x2 andtotal revenues givenby R(x)= 285x − 0.8x2,find the break-even points. (Enter your answers as acomma-...

Question

If a company has totalcosts C(x)= 14,000 + 15x + 0.2x2 andtotal revenues givenby R(x)= 285x − 0.8x2,find the break-even points. (Enter your answers as acomma-separated list.)

If a company has total costs C(x) = 14,000 + 15x + 0.2x2 and total revenues given by R(x) = 285x − 0.8x2, find the break-even points. (Enter your answers as a comma-separated list.)



Answers

Total cost is $C=8500+4.65 q$ and total revenue is $R=5.15 q,$ both in dollars, where $q$ represents the quantity produced. (a) What is the fixed cost? (b) What is the marginal cost per item? (c) What is the price at which this item is sold? (d) For what production levels does this company make a profit? (e) How much does the company make for each additional unit sold?

All right here we have to find the total profit for part a break even point for Part B. And so what we have to for part a is take your revenue minus your cost. And so we sub student What We know we know 40 x is our revenue, and we know that 15 X plus 3100 is our cost. We then combined like terms and do 40 minus 15 gives you 25 x constant is 3100 And that would be your tour roughed. Yeah, for part B, The break even point would be when, uh, the two functions equal each other and so we would have see of X Equals are of X and then we would sold for us once again plug in what? You know we have 15 X plus 3100. Is there a cost function and that has to equal our revenue, which is 40 X. I like to draw my chimneys or what I do the one side of the chimney I must do to the other side. Now we're going to isolate the variable X. So first we're going to move 15 x to the right hand side of the equal sign that eliminates some more chances. Amount on that side, and we get 25 X over here, and then we get 3100 upside 3100 remaining on third left said. And then the last step we have to do is divide both sides by 25 and so X would equal 124 number your break even point.

All right for this problem. We have two answers. We have the total profit we need to find and the break even put for part A. We're going to look at the break spurs or the total profit part. And to do that, we need to find our X minus sea of X. So we substitute in what we know for each function and each function. So our revenue is 40 X and our cost is 25 x minus 3100 plus 3100. So then we combine like terms and we get 15 X plus 3100. And that is your total profit for part B are break even. Point is, when we have our two functions equaling each other so we would have r of X equals C of X should be in red, and then we plug in what we know. So 40 x equals 25 x plus 3100. And then I like to do these things I call the chimney. So what I do to one side of the chimney I remember to do to the other side of the chimney or the equal sign. So first we're going to get all of our variables to one side. It's weird. It's attract 25 on both sides. 25 X, This cancels over here. And over here we'd have 15 X on the left side and 3100 left on the right side. Now, to isolate the variable, we have to divide both sides by our coefficient of 15 and we're left with X equals 124 which is your break even point.

All right for this problem. We have our cost function to be 15 x plus 3100 in the revenue function to be 40 x. So for part A, it asks us to find the total profit. And so to find the prophet you need, take your revenue and subtract your cost. So substitute in what you know, we know 40 X is their revenue, and we know that 15 X plus 3100 is our cost. But we have make sure this subtraction goes into the entire function. So we have 15 x minus 3100. We now combine like terms and we would get 25 x minus 3100 for our profit. For part B, you get this to a good spec. Part B. It asks us to find the break even point now is to answer to the break even point. There's the quantity and the cost. So this is when our revenue and our costs are the same. And so we know our revenue is 40 X. We know our cost is 15 X plus 3100. Now we need to isolate the variable X. So using inverse operations, we would subtract 15 X to get the variables on the same side. We would simplify that to 25 x equals 3100 and to continue our inverse operations to isolate the very will be divided by 25 on both sides in X equals 124. Now we're not done because I just gives us our quantity. We need to plug this into our revenue and see what that would cost us. So we have 40 times, 124 which would give us 4960. So our final answer would be 1 24 4000 960.

Hello. In this problem, we're given the cost on the revenue functions on. And we have several questions, questions to answer. So the first form is on the ray. Uh, when HQ using 500 when we have 500 units produce. What is the cost? What is the revenue we sell 500 units and do we have a profit? Okay, let's calculate how much See all 500 years, We, uh, replaced you with 576,000 plus Think times 500 which is 6000 plus 5000 which is 11,000. The revenue off selling 500 products is 12 firms 500 products, which is 60 with 0 $6000. The perfect function. The perfect function is defined as the revenue minus the the costs with both, the greater the revenue, then the ribbon you Then we have a negative profit. So the profit is minus 5000 Laws on you know the words we incur no profit. The company has a nonprofit. There is a loss of 5000. Those when a quantity or 500 units is produced. What happens when the number of units is five thousand's? See all five thousands equal six thousands plus 10 times 5000 which is 6000 plus 50. It's 56. Nothing close revving your 5000 I think so is 12 times 5000 which is four times I was 16. Of these three zeros is 60,000. Now we have a profit off 60 1000 minus 56 which is a plus. With that, as long as we have profit, we have oppression. So producing and selling 500 pieces incurs costs of learned 1000 arriving 6000 in the loss 5000 the costume will in producing 5000 units of 56 our laws. The revenue is $60,000 by selling 5000 units, but we should make a profit off 4000 balls. Okay, we now go to question be What is the break even point on to give a graphical interpretation? The break even point is the quantity Q. For which we have the The revenue off here ruin your selling que items is the same as the cost off, producing fewer items, incurring a profit off zero that is neither a profit or loss. So we equate two of you. We'll see if you're ambitious 6000 plus. Thank you. Subtracting. Thank you from both science. 12 months. Then it's two kids equal 6000 divide. But we have cube equals 3000 units produce no. At 3000 units produced. We have the revenue off 3000 which is the same. This cost off 3000 just is the simple one. Is this also 12 times 3000 wishes, maybe six $36,000 Is the revenue gained by selling 3000 years and equals the cost off, producing 3000 units. Representing this graphically, we will have, uh, see, we will have. You won't be horrible. Blacks and the price in those on the vertical access on would see we may have $10,000 here thing. 20,000 year. 25. 30,000 here on fourth. The option. So we have for the revenue function. Uh, this passes through 0.0. Um, a breaking points on the graph is going to be 3000 units produced. Really? All 3 36,000 So we have 3000 here, 35. 36 would be hit so they would meet at this point, but 3000 he thinks right So the graph of our graph of revenue would be so. Okay, this is the arcade. And, uh, for safety seeing zero C zero equal 6000 when we substitute. Given zero, we have 10 times here. Zero sales, 0 6000 sentence to be five or 6000 year, and you don't see it passes through the, uh, breaking point way. See if you to be this bringing alarm here. Okay, This point would be the breaking point on before the breaking point to see the costs are great at the revenue. The profits would be negative here. I mean, we were being going off. Ah, I'm talking about before 3000 years on if more than 3000 units of May, then way would have a positive Crawford. Because the revenue production is a sub. The cost function on discovers the whole problem. Help Baba


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