ALGEBRA 2 PROBLEM?? HELP?
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The Valley High School student council is sponsoring a dance. They anticipate that 500 students will attend. The ticket price is $3.00, and they estimate that for every $0.20 increase in ticket price, 25 fewer students will attend. What ticket price will maximize the student council’s profit?
A ---- $3.25
B ---- $3.40
C ---- $3.50
D ---- $3.80
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The returns (R) from the dance is: R =NxP where N is the number attending and P is the ticket price.
Now N=500-25(P-3.00)/(0.20) = 500 -125(P-3) = 875 -125P
So R=P(875-125P) = 875P -125P^2
For the maximum, dR/dP = 0 or 875-250P=0 or P=875/250 =7/2 =3.50