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# A baseball team plays in a stadium that holds 64000 spectators. With the ticket price at $9 the aver wrote... Express Lane Plus Posts: 485 Rep: 2 0 4 weeks ago  A baseball team plays in a stadium that holds 64000 spectators. With the ticket price at$9 the aver A baseball team plays in a stadium that holds 64000 spectators. With the ticket price at $9 the average attendance has been 29000. When the price dropped to$7, the average attendance rose to 32000. Assume that attendance is linearly related to ticket price. Attached file Thumbnail(s): You must login or register to gain access to this attachment. Read 50 times 1 Reply
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Educator
4 weeks ago
 Let x = the ticket cost reduction in $. The ticket price function will be: Price =$9 - x The demand function (number of spectators) is: p(x) = 27,000 + 5000x The revenue is: R(x) = (Demand)(Price)R(x) = (29,000 + 5000x)(9 - x) = 261,000 + 45,000x + 29,000x - 5,000x^2R(x) = $$261,000+74,000x-5,000x^2$$ To find the optimal revenue, take the derivative of R(x) wrt x, set it to zero, and solve for x.$$R'(x)=74,000-10,000x$$$$-74,000=-10,000x$$$$x=\frac{-74}{-10}=7.4$$Price = $9 - 7.4. Answer is$7.60.
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