2 For 1 Theatre Tickets
word problem involving quadratic functions… ?
I am doing an advance reading about functions… and i ahve this word problem that i couldnt figure out on how i will solve this problem.
an inquiry shows that 60,000 students will attend a theater play in one week if the ticket price is 40 dollars. Suppose that for every 2.50 dollars added to the ticket price, 2000 fewer students will attend the play.
1. What ticket price will give the greatest revenue for the week?
2. what is the approximate maximum possible profit for the week if the theater play spends approximately 1.5 million dollars to have the play showed for one week?
thanks!!! 
where did 1500000 come from?
for those who have answered already, i just wanna ask where did 1500000 come from?
1. Let x be the number of times $2.50 is added to the ticket price (and 2,000 fewer students attend).
Revenue for the week is (40+2.50x)(60,000-2,000x)
= 2.5(16+x)*2,000(30-x)
= 5,000(16+x)(30-x)
= 5,000(-x²+14x+480)
Thus the greatest revenue is given by the maximum of function -x²+14x+480. It is a quadratic function with a maximum of -b/2a= -14/(-2)=7. 7 is the value of x for which the revenue will be greatest. To answer the question, calculate the corresponding ticket price by adding $2.50*7 to the original $40=40+2.5*7=$57.50.
2. Profit=revenue-spendings.
Since spendings are fixed, maximum profit is obtained when maximum revenue is obtained as above, for x=7.
Max profit=5,000(-7²+14*7+480)-1,500,000
=$1,145,000.
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