the-total-cost-c-in-dollars-of-production-can-be-interpreted-as-an-area-if-the-cost-per-unit-cprim-2

Name: the total cost c in dollars of production can be interpreted as an area if the cost per unit cprim 2
Uploaded: 2020-06-15
Duration: 2 min 41 s
Channel: Numerade
Description: The total cost $C$ (in dollars) of production can be interpreted as an area. If the cost per unit $C^{\prime}$ (in dollars per unit) of producing $x$ units is given by $100 /(0.01 x+1)^{2}$, find the total cost of producing 100 units by finding the area under the curve of $C^{\prime}$ vs $x$.

Question

The total cost $C$ (in dollars) of production can be interpreted as an area. If the cost per unit $C^{\prime}$ (in dollars per unit) of producing $x$ units is given by $100 /(0.01 x+1)^{2}$, find the total cost of producing 100 units by finding the area under the curve of $C^{\prime}$ vs $x$.

Cinsy Krehbiel · Accepted Answer

given this cost function like to compare the marginal cost to the average cost. So the marginal cost That&#x27;s the first derivative. See prime of X. That&#x27;s going to be 0.2 x less 40 and the average cost is the cost to make X items divided by X. So if we take our function CFX and divide by X, we&#x27;re going to get 0.1 x squared plus 40 x less 3600 over X. And if we simplify that a bit will have 0.1 x less 40 plus 3600 over X. So this is our average cost. And let&#x27;s compare at 100 100 items, the marginal cost would be see prime of 100. That&#x27;ll be 0.2 times 100 plus 40 which equals 42. The marginal cost is 42 at X equals 100. The average cost at X equals 100. It&#x27;s going to equal the 0.1 times 100 plus 40 plus 3600 divided by 100 which equals 77. So we can see the marginal cost of ah 100 which equals 42 is less than the average cost to make 100 items, which is 77. If we were to make another item, the average cost for 101 items would be. This same function only will substitute in 101. I was 3600 divided by 100 and what? And that turns out to be 76.6, which is less than 77 so we can see that the average price goes down as the number increases.

Ankit Gupta · Answer

see every digital to see the rhetoric exit because to do point to excess choir plus 10 X plus five divided by XviD eggs You know the vertical s and told I take city close to zero slant from gold is giving us why is it questions you know, point to express train? There&#x27;s no any white intercept because we cannot put X equals 20 because X is always better than you. That&#x27;s fine. Or cemented additional points to a skit. The graph then get out. Look, something like this, which has one slanders and jokes. And one particle isn&#x27;t the minimum value of see every occurs at X equals 25 So number off units for cost to be minimum is it questo fight?

Gladys Fowler · Answer

I guess so for problem 59 we are given the function see of X equals 1500 plus three x plus 0.2 x squared plus 0.0 cause 0.1 x cubed So part a part B and part C are the three parts of number 59 Part a wants us to solve for C of tan and see of 100 Any time that you have a function of X like this and then you replace that X with a number will do exactly that same thing to solve for our problem. So to solve sea of 10 for a you would just replace X with 10 everywhere you haven&#x27;t XXII of 10 equals 1500 plus three times 10 plus 0.2 times 10 squared plus 0.1 times 10 and cubed. And now would you put that on your calculator? You should get 1532 and 10 cent and the N C. Of 100 is the same process. But this time with 100 so three times 100 plus 1000.2 times 100 squared plus 1000.1 times, 100 cubed and you should get 2100 dollars. Even so, for part B, it ask us to explain parts and see part B. You can write that sea of tan and see of 100. Both represent the cost in dollars, four the yards of 10 and 100. Um, we can also put we can add of a certain type of fabric. So if we get 10 yards of fabric or 100 yards of fabric, we have the cost in dollars for part A and in part C ask us to solve for C of zero now see of zero would mean that we have zero yards of this fabric and that would be the fixed cost of other running our company. Whether that be a print company or some kind of advertising company, maybe for our fabric or clothing. Whatever have you see of zero is going to be our fixed cost. So that would just be where we input zero for X, so cf zero equals 1500 class three times zero plus 0.2 time zero squared plus 0.0 or one time zero cute and I was gonna put that answer down here and see a zero is going to be a 1500. Because if you look at our problem, the number 1500 is the only one without a variable eggs. That means that is the only number that is not going to inevitably turn into zero with multiplication of zero. Okay, so at that point part, a part B and part C. So we are finished.

Charlene Bische · Answer

Yeah.

Amy Jiang · Answer

Okay, so we&#x27;re giving a marginal cost function as well as two units. Costs $5.50. So that is our cost function. Evaluated at 20 to 5. What? 50. Okay. And we have to find our cost function. So notice here that we have the derivative of our cost function, so we can just take the integral of that. Your evidence. And that should give us our cost function. Plus some constant k. Okay, so let&#x27;s solve for that. So starting with the integral of X plus one over X squared, we get the falling. Let&#x27;s use our some world just work out up into two intervals. I will also be right one over X squared as a negative exponents. Okay, I know using a powerful begets extra car to over to what exit? Power of negative one over negative one. So that&#x27;s equal to negative one over X. That&#x27;s okay. Okay. And this is our cost function with an arbitrary constants, kid. Another tier of that we have see of two is equal to 5.5. So let&#x27;s put that into find RK So we have five points. 50 is equal to I want you to. So that&#x27;s two squared off to one. It&#x27;s 1/2 plus K. So that gives me four of the two, which is two minus one have plus K and 5.5. So too, is for over two. That&#x27;s equal to three over to K and 5.5. So 5.5 minus 3/2 gives me four. So we have our constants is equal to four. Okay, so let&#x27;s just replace R K value with that for so this is equal to our cost function.

Problem

A cam is designed such that one face of it is des…

Problem 46 Easy Difficulty

The total cost $C$ (in dollars) of production can be interpreted as an area. If the cost per unit $C^{\prime}$ (in dollars per unit) of producing $x$ units is given by $100 /(0.01 x+1)^{2}$, find the total cost of producing 100 units by finding the area under the curve of $C^{\prime}$ vs $x$.

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