Hint Optimisation Question

[Procrastinate]

A manufacturer can sell x CD players per week at d dollars per item, where
x = 600 - 3d

Production costs (in dollars) are given by:

C(x) = 600 + 10x + 0.4x²

How should the CD players be priced in order to maximise profits?




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I have tried a variety of ways but none of them have shown much progress:

dx = 600t - 3d²

Then it doesn't make sense when I take this away from P because there are then three variables.
I have also tried re-arranging x = 600-3d to x-600/-3 but that has shown no success.


Please, could anyone provide some productive hints?

 

[Office_Shredder]

It's not clear in your post what you're trying to do. Do you have an equation that gives the profit of the manufacturer based on d? Remember that profit is revenue minus cost, and that the revenue is the price times the number of CD's made