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#1 2007-07-25 21:53:43

Identity
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Registered: 2007-04-18
Posts: 934

Quadratics and Ticket Sales

The local theatre has a full house of 1050 nightly and charges $15 per ticket. The manager estimates that the ticket sales would decrease by 50 for each $1 increase in the ticket cost. What ticket price should be charged for maximum income?

Last edited by Identity (2007-08-06 01:07:49)

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#2 2007-07-25 22:37:10

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Quadratics and Ticket Sales

Denoting the price increase as x, the amount of tickets sold is given by (1050-50x), or 50(21-x) if you prefer, and the price per ticket is (15+x).

The total revenue is then 50(21-x)(15+x).
Differentiate this and equate to 0 to find the maximum.


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#3 2007-07-25 22:38:51

Identity
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Registered: 2007-04-18
Posts: 934

Re: Quadratics and Ticket Sales

Thanks mathsyperson

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#4 2007-07-26 02:39:52

John E. Franklin
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Registered: 2005-08-29
Posts: 3,588

Re: Quadratics and Ticket Sales

Be careful because if you differentiate, and set to zero, you might be finding the minimum.  But since it is x * -x, that parabola open down, so it probably is a maximum, sorry for confusion.


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#5 2007-07-26 02:46:27

luca-deltodesco
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Registered: 2006-05-05
Posts: 1,470

Re: Quadratics and Ticket Sales

in the event that parabola opened up, the question would have been impossible since the maximum would be undefined

Last edited by luca-deltodesco (2007-07-26 02:46:49)


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#6 2007-08-02 02:40:17

HallsofIvy
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Re: Quadratics and Ticket Sales

There is no need to differentiate.  Since the object function is quadratic, just complete the square.

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