400 people came to last years winter play at a high school. The ticket price was $5. This year, the Drama Club is hoping to earn enough money to take a trip to a Broadway play. They estimate that for each $0.50 increase in the price, 10 fewer people will attend their play. (determine how much the tickets should cost in order to maximize the income from this years play) x = #of $.50 price increases.
2007-12-06 09:45:33 · 1 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
400 ( = 400 - 10*0) tickets will be sold if x=0 (price = $5.00 = $5.00 + 0.50*0)
390 ( = 400 - 10*1) tickets will be sold if x=1 (price = $5.50 = $5.00 + 0.50*1)
380 ( = 400 - 10*2) tickets will be sold if x=2 (price = $6.00 = $5.00 + 0.50*2)
Do you see the pattern? If there are x price increases of $0.50, the number of tickets sold will be (400 - 10*x) and the ticket price (in dollars) will be (5 + 0.50*x).
The total revenue R (in dollars) is the number of tickets sold, times the ticket price:
R(x) = (400 - 10x)(5 + 0.5x)
Your task, now, is to maximize R.
2007-12-06 11:11:38 · answer #1 · answered by Ron W 7 · 0⤊ 0⤋