An art exhibit sells 80 tickets per day at $10 per ticket. For every $1 increase

Question

An art exhibit sells 80 tickets per day at $10 per ticket. For every $1 increase in the price per ticket, the manager expects to sell 4 fewer tickets per day. Use this information for the following problems, and justify your reasoning:

a.) Let T(p) be the number of tickets the manager will sell if they charge $p each and let R(p) be the daily ticket sales revenue. Find formulas for T(p) and R(p) (assuming a linear relationship between price & sales).

b.) What price should the manager charge per ticket to maximize their daily ticket sales revenue? Using this price, calculate the total numer of tickets sold (daily) and the total daily revenue.

Explanation / Answer

a. T(p) = 80 -4p

Revenue = (10+p) * T(p)

R(p) = (10+p)(80-4p) = -4p2+40p+800

b.R'(p)= -8p+40

R'(p)=0

-8p+40=0

    p=5

total number of tickets sold, T(p) = 80-4(5) = 60

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