-Write a formula fro the revenue, \'R\', as a function of the number of 10 cent
ID: 2880333 • Letter: #
Question
-Write a formula fro the revenue, 'R', as a function of the number of 10 cent decreases in price 'x' if 'A' tickets are sold at a price of 'p' dollars.
-Solve p(x)=0 and explain what it means in the context of the situation.
-Solve A(x)=0 and explain what it means in the context of the situation.
-Solve R(x)=0 and explain what it means in the context of the situation.
-Expand R(x) into the form y=ax2+bx+c and interperate the parameters a, b, and c.
Let p denote the price of the theater's movie ticket and assume that the theater seats 2,000 people in total throughout all of it screen rooms. Suppose that with ticket prices at $12 the average attendance last month was 1,000. Further suppose that the theater conducted a survey and discovered that for every 10 cents the ticket price dropped the theater would attract another 20 moviegoers.Explanation / Answer
Average film goers =1000
Capacity = 2000
Let x times the price be decreased.
Then price = p(x) = 12-0.1 x
p(x) =0 gives 0.1 x =12 or x =120
120 times 10cents decreased so that price of ticket became zero.
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A(x) = No of tickets sold = 1000+20x
A(x) =0 gives x = -50
i.e. 50 times 10 cents increased no of movie goers will be nil
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R(x) = A(x) P(X) = (12-0.1x)(1000+20x)
= 12000+140x-2x2
R(x) =0 implies either x = 120 or x = -50
120 times decreased or 50 times increased.
R(x) = 12000+140x-2x2
Quadratic with a = -2, b =140 and c = 12000
Even when no change is there in price, Revenue will be 12000 (same as for last month)
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