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Blue Jays tickets cost too much! The good folks in charge of Toronto Baseball
have found that for every 50-cent decrease in the average ticket price, 300 extra
tickets will be sold. Right now, the average price of a ticket is $80, and they sell an
average of 30,000 tickets per game. The capacity of the Rogers Centre is 49,282.
Determine the optimal ticket price that maximizes revenue, the new number of
tickets sold, and the amount of extra revenue the Blue Jays will take in per game
when compared to the current revenue.

Respuesta :

The optimal ticket price is $ 65.The amount of tickets sold is 39000 and the amount of the extra revenue will be $ 135000.

What is the objective function?

The objective function is simply an equation that represents the goal production capability that relates to maximizing profits from manufacturing.

Current revenue;

⇒ 80 × 3000 = 240000

From the given condition the price decrease by 0.5 times. So that the ticket sold will be 300 times the cost. The inequality relationship is found as;

30000+300x  49282

x≤64

The revenue value is found as;

y = ( 80 - 0.5 x )(30000+300 x)

y=-150 x²+9000 x+2400000

The value of x is found as;

[tex]\rm x= \frac{9000}{150 \times 2 }\\\\ x=30[/tex]

Hence, the optimal ticket price is $ 65.The amount of tickets sold is 39000 and the amount of the extra revenue will be $ 135000.

To learn more about the objective function, refer to the link;

https://brainly.com/question/15830007

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