Question

The marginal cost function of producing q mountain bikes is 600/0.3q+5.
If the fixed cost in producing the bicycles is 2200 , find the total cost to produce 30 bicycles.
If the bikes are sold for 205 each, what is the profit (or loss) on the first 30 bicycles?
Find the marginal profit on the 31st bicycle.

Answer 1

Marginal cost is the change in total cost that arises when the quantity produced changes by one unit.(In another word derivative of cost wrt unit)

So we integrate to get Cost function
\[\int_0^{30} \frac{600}{0.3 q+5} \, dq\]
we get 9798.66 from integration.

We add that to fix cost 2059.23+2200=4259.24
So 4259.24 is the cost.
Revenue from selling the bike is 205*30=6150
Profit=Revenue-Cost
6150 - 4259.24=1890.76

Now marginal Profit
Marginal profit is the term used to refer to the difference between the marginal cost and the marginal revenue for producing one additional unit of production.
Marginal Profit=Marginal Revenue-Marginal Cost

Marginal Cost=600/0.3q+5.
Let's plug in 31 to get 41.958

Revenue= 205q
Marginal rev=205
Marginal Profit = 205-41.958=163.042

Answer 2

I hope I got the equation for marginal cost correct

Answer 3

where did you get the 2059.23 from though?

Answer 4

I got 2059.23 from integration but I mistakenly wrote 9798.66

Answer 5

oh okay! this all makes so much sense! I was approaching it soo differently. thank you soooooo much for your help, I deeply appreciate it!

Answer 6

You're welcome, It is strange to put that much economic related problem in Calc I. I didn't have to do any of that when I took Calc I,II, or III

Answer 7

oh my goodness, really?!

Answer 8

It is like you are economic class or something. Most of our application problem involve find area and volume

Answer 9

when I posted the last problem, I got the same reply. the class itself is called Calc 1, for the Social sciences.

Answer 10

At my school we have a class called Business Calc for Business major, I think they deal with things like that.

Answer 11

I recommend MIT lectures online, I learned all calculus(and physics) from them instead from my school.
http://www.youtube.com/watch?v=jbIQW0gkgxo

Answer 12

oh thanks so much for the site, i'll make sure to do so:) &that makes sense. where do you go to school?

Answer 13

University of Illinois

Answer 14

goood school, you should be proud of yourself:)

Answer 15

Engineering courses are good but math professor sucks

Answer 16

Oh my, I feel like math is such a profound field though. Like if you understand it, often it can be hard to explain to others. feel me?

Answer 17

Yes, especially calculus; you have to understand your own way to master it.Especially in Multivariable calc when it make no sense when prof start drawing three dimension surface on the board

Answer 18

What are you planning to major in?

Answer 19

I agree completely and admire those that do.oh my goodness, 3-d math is quite interesting I must say. I've only seen it. i"m actually going to be a sophomore in college, I major in psychology:) and yourself?

Answer 20

elec engineering

Answer 21

I am going to be sophomore too

Answer 22

that's awesomeee! good for youu, field of opportunityyy, i have some friends majoring in that, i know you will go far even though we haven't met, aha i can just tell:)

Answer 23

I hope so, trying to graduate quick; taking summer class at community

Answer 24

oh I see, that's good though, maybe an internship soon?

Answer 25

I was gonna but I have only taken one engineering course. So I don't know much,lol

Answer 26

haha everything in time:) what's your background, if you don't mind my asking?

Answer 27

as in ethnicity? Well my parent emigrated from Burma so Burmese

Answer 28

that's so neatttt:)& yes that's what I was referring to, ahaha.

Answer 29

What's yours?

Answer 30

half-Brasilian & a mix of other things:)

Answer 31

cool, nice to meet you

Answer 32

so nice to meet you too! you seem like such an intriguing person from what i know:)

Answer 33

Thanks, you too

Answer 34

you're welcome&thanks so much!:) i hope that you're enjoying your summerr!:)

Answer 35

I am, you have a great summer

Answer 36

good to hear it, thankyou:) i appreciate your kindness!