[Please help] Calculating optimal price, profit & revenue

[Emil24]

Hello everyone,
I am having difficulties finding the optimal price, profit and revenue in an assignment.
The questions reads:

When it is being sold to a price of $30/pcs., it sells 25 pcs./day. The price elasticity Ep is 3.
Find the optimal price, revenue and profit on sale of product on one ticket.

The fixed price is 500. I do have average value cost, total value cost, total cost, average total cost and average fixed cost calculated. But what is the next step?
I am really desperate for help - been looking on this over and over.

It is given, that:


Q 0 5 10
MC 11 10,52 10,08

I hope a friendly soul out there has a little bit of extra time to help me out on this one, would be truly appreciated!
Thanks in advance.

-Emil

 

[kys916]

It's easier if you use calculus. Fast simple solution using solver.

A1 30 [price]
A2 25 [q]
A3 -3 [E]
A4 X (the number your trying to solve)
A5 (A1+X) *(A2+E*X)
Use Solver Maximize A5 by Changing A4
A1-A4 = Price

 

[Emil24]

It's easier if you use calculus. Fast simple solution using solver.
A4 X (the number your trying to solve)
Use Solver Maximize A5 by Changing A4

First off all, I am truly grateful for the reply.
Now, could you please go into details about the thing with A4? Can't really see what A4 should contain?

Anyhow, there should be a formula to calculate the optimal price, profit and revenue, right? I'm a bit lost here...

 

[kys916]

A4 is the optimal price increase or decrease.

I totally forgot the formula for it, so you should google or check a textbook. Basically beginner level calculus (first year undergrad)

AVC and Fix cost doesn't matter. Only thing that matters is variable cost. Just subtract the variable cost to the price since profit is (P-VC)*Q-FC.
FC doesn't depend on q if you think about logically or mathematically. Your maximize q if your doing calculus.