Optimizing Cost per Unit with Calculus

[Elihu5991]

Homework Statement

REFER TO IMAGE

Homework Equations

SEE ABOVE

The Attempt at a Solution

I haven't been able to start this question. I'm wondering how to find the 'average cost per unit'.

 

[SteamKing]

What is the definition of 'average'?

 

[Elihu5991]

I'm aware of what average means, though how would I find it with calculus? That, I'm not familiar with. I've done averages with actual numbers, not variables. Should I first differentiate it or do something else?

 

[DrClaude]

If it costs C to build x units, what is the cost per unit?

 

[Elihu5991]

Your asking me what the question is asking in a simplified manner. I'm asking how to find the average. I'm unfamiliar with finding it with function specified.

 

[DrClaude]

I'm just trying to get you to find the answer yourself. Put it in numbers if it helps.

If it costs $100 to build 10 units, what is the cost per unit?
If it costs $50 to build 1000 units, what is the cost per unit?

How do you solve those? Can you use your solution to find how to express generally (in terms of C and x) the average cost?

 

[Elihu5991]

Wouldn't there be a relationship, so I would first have to differentiate it? Thus, that function would then be the one for the average cost per unit?

But it's asking for an actual value for x, which is throwing me off. Would I need to follow common procedure like other optimisation questions?

 

[Ray Vickson]

Homework Statement

REFER TO IMAGE

Homework Equations

SEE ABOVE

The Attempt at a Solution

I haven't been able to start this question. I'm wondering how to find the 'average cost per unit'.

For the given const function, what would be the total cost of x units? What would be the corresponding cost per unit? (Forget the word 'average'; just look at the cost per unit).

 

[Elihu5991]

Will it be x^3 or cubed x?, since the function is "wrapped" to ^3?

 

[Ray Vickson]

Will it be x^3 or cubed x?, since the function is "wrapped" to ^3?

Which message/question are you responding to? Please use the correct "response" panel.

 

[DrClaude]

Forget about the equation. We need to take one step back. Please start with answering post #6.

 

[Elihu5991]

@Ray

Sorry I'm on the iPad at the moment, so I can't just do that. I forgot to use the alternative.

I was replying to you.

 

[Elihu5991]

@DrClaude

I don't now how to find an actual value of x when there's only one real number in the equation: 10?

 

[Ray Vickson]

@DrClaude

I don't now how to find an actual value of x when there's only one real number in the equation: 10?

What are you not seeing? If x = 2, what is the total cost? What is the cost per unit? If x = 10 what are the total cost and cost per unit? If x = 7 what are the total cost and the cost per unit? If x = 25 what are the total cost and the cost per unit?

If you can figure out the cost per unit when the value of x is given, just do the same thing when the value of x is not given.