SOLUTION: The school musical will be held in a hall that has a seating capacity of 600. In the past, the musical committee has sold tickets for $10 each and tickets have always sold out.
Question 1141780: The school musical will be held in a hall that has a seating capacity of 600. In the past, the musical committee has sold tickets for $10 each and tickets have always sold out.
The committee is planning to increase the cost of the ticket price but they are concerned because they predict that for each $1 rise in the ticket price they will sell 25 less tickets. They have come to you for advice.
Prepare an analysis summarising the relevant information for the committee with a recommendation for the new ticket price. The committee is also interested to know the expected increase in revenue
You can put this solution on YOUR website! Let = the number of $1 increases in the ticket price
Their prediction is that will be the number
of tickets they will sell at a price of dollars each
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Let = revenue from sales of tickets
What value of gives them the maximum revenue?
The plot of is a parabola with a maximum n-value at
When , revenue is a maximum
$7,225 is the maximum revenue they can make.
Revenue will increase for each $1 increase in ticket price
until the tickets cost $17
After that, Revenue will decrease.
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Here is the plot of ( n, R )
