Problema Solution
a theater contains 500 seats for an upcoming talent show, the theater manager plans to sell $4 and $5 tickets. he must sell at least 200 $4 tickets and 100 $5 tickets for the show to be produced and he must bring in at least $2000 to break even. how many tickets at each price should be sold to maximize income? what is the maximum income ?
Answer provided by our tutors
let
x = the number of $4 tickets
y = the number of $5 tickets
we have the following system of inequalities
x + y <= 500
x >= 200
y >= 100
4x + 5y > = 2000
click here to see the graph of the system of inequalities
from the graph we find the following vertices:
(375, 100)
(400, 100)
(200, 300)
(200, 240)
how many tickets at each price should be sold to maximize income? what is the maximum income ?
(375, 100) 4*375 + 5*100 = 2000
(400, 100) 4*400 + 5*100 = 2100
(200, 300) 4*200 + 5*300 = 2300
(200, 240) 4*200 + 5*240 = 2000
to maximize the profit the theater manager should sell 200 $4 tickets and 300 5$ tickets.
the maximum income is $2,300.