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“Know guys good applications of calculus question for you today. We ve got a company company that makes x washing machines per. Day now the cost to them of producing washing machines is. 2000 plus 100x minus 01 x squared now we re asked to do three things the first thing being that we ve got to find the average cost per machine of producing the first 100 washing machines.

It s the second being we ve got to show that the marginal cost when producing a hundred washing machines per day and the third thing is we ve got to show that the marginal cost when producing a hundred washing machines per day is approximately the cost of producing one more washing machine after the first 100 washing machines have been made so part c is quite a mouthful. But basically we ve got to show that the cost of making the hundred and first washing machine is equal to the marginal cost at a hundred washing machines. So let s just start with part a then okay so the part a to find the average cost per machine of producing the first hundred washing machines all we re going to do is find the total cost of producing a hundred washing machines and divide. It by a hundred so basically the way that we re going to do this.

So. Let s just write down part a is we ve got the average total cost is going to be equal to the cost of producing a hundred washing machines divided by 100 now if i m gonna do all of the working out guys. What i m gonna do is i m just gonna serve a hundred into our cost. Function so we have two thousand.

Plus a hundred times 100 minus..

01. Times. A hundred squared and all of that guys is going to be divided by 100 great so if i calculate this guys i m gonna get eleven thousand divided by 100 which is equal to one hundred and ten dollars per per washing machine okay guys so on to part b now we re asked to find the marginal cost of producing a hundred machines per day so the marginal cost guys is the cost added by producing one additional unit of the product or service. So it s the cost of the next item that we re going to produce so the way we find this mathematically guys is if we have a cost function like this one.

Which is differentiable can take the first derivative of that cost function with respect to the quantity produced or we can find the derivative of cost with respect to x. So in this case when we re producing a hundred machines per day the marginal cost of us asking us to find will just write be the marginal cost. Which is asking us to find is that a hundred is going to be equal to the derivative of the cost function with respect to the amount that we re producing cool so what we re going to do and we re going to evaluate that at x equals. 100.

So what we re going to do first is let s take the first derivative of our cost function and this is going to be equal to one hundred subtract. 02 times x great so now what we want to do guys is to find the answer for part b ie. The marginal cost when we re producing a hundred machines per day is simply evaluate this when x equals 100. So we re going to go well d.

C of..

X. Dx when. X. Equals 100 is equal to 100 minus.

02. Times. 100. Which is equal to 80.

Great okay now on to part c. Which were asked to show the marginal cost. When producing a hundred washing machines per day is approximately the cost of producing one more washing machine per day after the first 100 washing machines had been made and it gives us a hint where we calculate the latter cost directly so basically guys what it s asking us to do is show that the cost of producing a hundred and first machine is approximately equal to the marginal cost when x is equal to 100. So basically what we re going to do is to find the cost of the hundred and first machine.

What this is going to be equal to is the cost function evaluated at 101..

Minus. The cost function evaluated at 100 and here guys. What we re going to do is we re gonna simply enter 101 into this function and a hundred into this function so when we enter 101 into this function. I get.

Eleven thousand and seventy nine dollars ninety and from part. A we know that the cost of reusing 100 james is. 11000 now when i do this subtraction guys i get 7990 and from here guys. What we basically then have to show that this is approximately equal to the marginal cost at a hundred machines per day so the marginal cost at a hundred machines is equal to.

80 and this is approximately equal to 7990. So we can say that we ve shown that the marginal cost. When producing a hundred machines. Which is this number here 80 is approximately equal to the cost of producing the one hundred and first machine which is 7990 so what you re gonna find guys is as you continue to produce more and more machines per day the cost of producing the next machine or the marginal cost will continue to decrease.

And this is basically the economies of scale argument ie that the bigger..

A firm is or the bigger a production processes. The cheaper that they can produce things per unit. And that s because the fixed costs as a proportion of the total costs become less and less and less so hope. The video helped guys if it did give it a thumbs up i d really appreciate it if you subscribe to my channel.

I put out new videos most days on economics chemistry physics and a host of other subjects. If you have any ideas for any videos that you d like to see me do please leave them in the comment section. Below. I d really appreciate that i m always on the lookout for new video ideas until next time guys just keep practicing your maths maths is definitely a practice makes perfect kind of subject if you keep bashing your head against the wall eventually the wall will fall down it s just a matter of time but just keep practicing practicing practicing.

But most of all guys keep enjoying yourselves. I hope to see you again sir ” ..

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description:

MARGINAL COST:

The marginal cost of production is the change in total cost that comes from making or producing one additional item. The purpose of analyzing marginal cost is to determine at what point an organization can achieve economies of scale. The calculation is most often used among manufacturers as a means of isolating an optimum production level.Manufacturing concerns often examine the cost of adding one more unit to their production schedules. This is because at some point, the benefit of producing one additional unit and generating revenue from that item will bring the overall cost of producing the product line down. The key to optimizing manufacturing costs is to find that point or level as quickly as possible.

AVERAGE COST:

In economics, average cost and/or unit cost is equal to total cost divided by the number of goods produced (the output quantity, Q). It is also equal to the sum of average variable costs (total variable costs divided by Q) plus average fixed costs (total fixed costs divided by Q).This calculus video tutorial explains the concept behind marginal revenue, marginal cost, marginal profit, average cost function, price and demand functions. It shows you how to find the production level to minimize the average cost as well as how to find the minimum average cost so as to maximize the profit of a company. This video contains plenty of examples and practice problems.

Here is a list of topics:

1. Cost Function – The price to a produce a number of items

2. Average Cost – The average price to produce a single unit

3. Production Level – The number of units or x

4. Marginal Cost – Derivative of the Cost Function

5. Marginal Cost represents the increase in total cost to produce one extra item

6. Minimizing Average Cost Function – Finding The Production Level and the Minimum Average Cost

7. Price Function or Demand Function – The selling price of an item as a function of x

8. Supply vs Demand – Inverse Relationship – Business u0026 Economics

9. Business Calculus – Revenue = Price Function x Number of Units (x)

10. Marginal Revenue, Marginal Cost, and Marginal Profit

11. Maximizing Profit – Finding the maximum value using the derivative function

tags:

marginal revenue, marginal revenue and marginal cost, cost, marginal revenue calculus, marginal cost, average cost, marginal profit, demand function calculus…