Mike can do a maximum of 4000 push-ups a week. His "fitness" index is given by the equation F = (2/5) (3000 - p)(p - 60), where F is his fitness index and p is the number of push-ups Mike does during one week. Which of the following represents the number of weekly push-ups that will maximize his fitness index?
(A) 1530
(B) 1580
(C) 3000
(D) 3100
(E) 3200
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find p such that F is max. The denominator must be small, and the numerator must be large.
ReplyDelete3000 - p >= p - 60
3060 >= 2p
p <= 1530
A is the answer.
Another way is to plug the numbers for (3000-p)/(p-60)
F=2/5*(3000p-1800-p^2+60p)
ReplyDeleteIdeally d2f/dp2 should be negative for maximizing a function.
df/dp=0 calculate value of p
3000-2p+60=0
p=1530
d2f/dp2=-2 (means maxima)