Problema Solution
At a price of p dollars per ticket, the number of tickets to a rock concert that can be sold is given by the demand model N= 20p+7000. At a price of p dollars per ticket, the number of tickets that the concerts promoters are willing to make available is given by the supply model N=10p+5800.
A. How many tickets can be sold and supplied for $35. per ticket?
b. Find the ticket price at which supply and demand are equal. At this price, how many tickets will be supplied and sold?
A. At $35 per ticket,____tickets can be sold at $35 per ticket,___tickets can be supplied.
b. When supply and demand are equal, the tickets price is $___per ticket.
When supply and demand are equal,____tickets are sold and supplied.
Answer provided by our tutors
A.
substitute 25 for p in the demand model
N = 20p + 7000
N = 20(35) + 7000
N = 700 + 7000
N = 7700
substitute 35 for p in the supply model
N = 10p + 5800
N = 10(35) + 5800
N = 350 + 5800
N = 6150
So at $35 per ticket, 7700 tickets can be sold and 6150 tickets can be supplied
B. set the supply model equal to the demand model and solve for p
20p + 7000 = 10p + 5800
20p + 1200 = 10p
1200 = -10p
-120 = p
Since the number of tickets cannot be negative, the supply and demand will never be equal.