The profit, $P, per item that a store makes by selling n items of a certain type each day is P=40 (n+25)^1/2−200−2n.

Find the number of items that need to be sold to maximise the profit on each item.

What is the maximum profit per item?

Hence, find the total profit per day by selling this number of items.

Question

The profit, $P, per item that a store makes by selling n items of a certain type each day is P=40 (n+25)^1/2−200−2n.

Find the number of items that need to be sold to maximise the profit on each item.

What is the maximum profit per item?

Hence, find the total profit per day by selling this number of items.

anonymous · Answer

Is that "...^(1/2) -200 -2n or
"...^(1/2 - 200 - 2n)?

anonymous · Answer

How many items did she sell?

anonymous · Answer

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anonymous · Answer

One could, through trial and error, figure it out, but I want to do it algebraically. Hmmm, this is an interesting one :) Maybe we should isolate n

anonymous · Answer

This would be easy using differentiation. setting the derivative to 0 gives n=75.
If you prefer not using calculus, substitute n+25=x^2, x>0. Then the profit is a quadratic in x and you can complete the square to find the maximum. If you want more details, write back.