Determining Total Cost for Alexis

[ProfessorHopk]

Heyy everyone! I could really use a hand tonight with this Total Cost calc problem. I'm suppose to solve for Q in the equation below but I don't know how it works... :/

Homework Statement

TC = Q/2 H[1-d/P] + (D/Q)S + P*D

I'm wondering if you can solve for Q?

Q = ?

dTC/dQ = ?

Homework Equations

My instructor also gave me these two equations but I have no idea if they're relevant..?
dy/dx = nx ^n-1

y = xⁿ

The Attempt at a Solution

I'm stumped at where to even begin. I would love some help from a fellow human! ;)

Thanks so much!
- Alexis

 

[Ray Vickson]

Heyy everyone! I could really use a hand tonight with this Total Cost calc problem. I'm suppose to solve for Q in the equation below but I don't know how it works... :/

Homework Statement

TC = Q/2 H[1-d/P] + (D/Q)S + P*D

I'm wondering if you can solve for Q?

Q = ?

dTC/dQ = ?

Homework Equations

My instructor also gave me these two equations but I have no idea if they're relevant..?
dy/dx = nx ^n-1

y = xⁿ

The Attempt at a Solution

I'm stumped at where to even begin. I would love some help from a fellow human! ;)

Thanks so much!
- Alexis

Can you state exactly what is the question? If you are given TC and want to find Q, then (assuming the other quantities H,P,d,S are known) you have a quadratic equation in Q to be solved. Just use the formulas you learned in school. If, however, the problem is to find the Q that minimizes TC, then you have a calculus problem.

Anyway, this looks like a single-period inventory control problem for a system with finite production rate. Normally in such problems we want to know the economic production quantity Q.

RGV

 

[ProfessorHopk]

To clarify I'm trying to find Q that minimizes TC.

 

[haruspex]

dTC/dQ = ?

If TC has a local maximum, or minimum, or inflexion at Q=q then dTC/dQ will be zero at Q=q. And conversely.

My instructor also gave me these two equations but I have no idea if they're relevant..?
dy/dx = nx ^n-1
y = xⁿ

To clarify, that should read:

If y(x) = xⁿ then dy/dx = nx ^n-1.​

And yes, it's relevant. You will also need
d(y(x)+z(x))/dx = dy/dx + dz/dx
d(k y(x))/dx = k dy/dx, where k is constant.
Can you write the equation for TC as a sum of functions of the form k Qⁿ?

 

[ProfessorHopk]

Can you write the equation for TC as a sum of functions of the form k Qⁿ?

I'm not sure exactly. Can you show me please? :)

XOXO - Alexis

 

[haruspex]

TC = Q/2 H[1-d/P] + (D/Q)S + P*D = (1/2 H[1-d/P])Q¹ + (DS)Q^-1 + P*D*Q⁰

 

[ProfessorHopk]

Ok that makes sense. So can you write out how to solve for Q?

XOXO

- Alexis

 

[Ray Vickson]

Ok that makes sense. So can you write out how to solve for Q?

XOXO

- Alexis

We are not allowed to do your homework for you, by the rules of this forum. In fact, you are supposed to show some attempt to do the problem yourself, and you have not done that.

RGV