Interest surveys performed by the promoter for the local band produced these data about relation between concert ticket price and ticket sales. Venue being considered is call "the jazz shack", it can accommodate 650 concert goers and costs $1000 to book the room. Suppose there are no other sources of income and no other cost for promoter.
1. Survey found that if tickets price $5, they could sell 600 tickets for concert. Two other data points (12,320) and (15,200) were found from survey as noted. Write the linear equation for projected ticket sales (number of tickets) T, as the function of ticket price p.
2. Use equation from #1 to express anticipated revenue R from ticket sales as the function of ticket price p. Recall that Revunue = (price per item) * (quantity of items sold).
3. Using quadractic equation from #2, find what prices charged per ticket would cause revenue to be zero.
4. Determine vertex of the model #2. Find predicted maximum revenue? what price would maximize projected revenue? Draw the detailed graph of the revenue model from #2 labeling intercepts and maxima.
5. how many tickets would require to be sold to maximize revenue?
6. what ticket price would sell out jazz shack? what revenue would bring?
7. You were told "it can accommodate 650 concert goers and costs $1000 to book room". Profit is stated as revenue-cost. Find profit equation as the function of price? Find maximum profit?
8. Assume they give you the choice of charging the flat rate of $1000 of 30% of revenue. what would be your profit function if you selected 30% option instead? what would be max profit?
9. Graph both profit functions together. Notice one is better (higher) for definite prices and then other model becomes better for other prices. what range of prices is flat $1000 charge better than 30% option? you may illustrate graphical work or solving the equation as justification for answer.