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m0286

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The goodfood catering company finds that competitors cater lunch for a group of 100 people for $5 each. The manager of Goodfood calculates the for each 25 cent discount per lunch, its possible to sell an additional 10 lunches. If each lunch costs goodfood $2 to prepare, how many lunches should be prepared to maximize profit.

This is what I got so far:

let P represent profit, let x represent # of discounted of lunches

P=(3-0.25x)(100+10x)

=-2.5x^2+5x+300

for the derivative i got x=1.

When i substituted that into the above equationi got:

=-2.5(1)^2+5(1)+300

=302.5 HERES WHERE I AM LOST!

Is this 302.5, the amount of profit they make or is this the number of lunches they should make to make greatest profit.?