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m0286
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I am stuck on a calculus problem.. I have most of the answer but I suddenly got confused, and can't figure it out any further, the question is:
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.?
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.?