The quantity demanded x for a product is inversely proportional to the cube of the price p for
p 1.
When the price is $10 per unit, the quantity demanded is 125 units. The initial cost is $120 and the cost per unit is $4. What price will yield a maximum profit? (Round your answer to two decimal places.) I'm not sure how to do this, can somebody please help explain this to me?

Question

The quantity demanded x for a product is inversely proportional to the cube of the price p for 
p > 1.
 When the price is $10 per unit, the quantity demanded is 125 units. The initial cost is $120 and the cost per unit is $4. What price will yield a maximum profit? (Round your answer to two decimal places.) I'm not sure how to do this, can somebody please help explain this to me?

tkhunny · Answer

"The quantity demanded x for a product is inversely proportional to the cube of the price "

This should speak to you directly and say this: $x = \dfrac{k}{p^{3}}$

anonymous · Answer

x=k/(10^3)

anonymous · Answer

or would it be x=k/(120^3)

tkhunny · Answer

125 = k/(10^3) -- Solve for k

anonymous · Answer

soo would I multiply both sides by k? and then divide both by 125?

tkhunny · Answer

That makes no sense.  Why not just multiply by 1000 and be done with it?

anonymous · Answer

ooh, yeah, that would be easier

anonymous · Answer

I have bad math dyslexia and mess up processes all the time, this is why i need help with simple algebra

radar · Answer

So what is the price that maximize profits.  For amount shown
125*4 + 120 = $620 cost
Gross received $1250.0 profit = $1250 - $620 = $630.00

radar · Answer

What is the problem asking of you??