Let the number of reserved tickets = x
Let the number of lawn seats = y
Constraint functions:
Maximum capacity means
For concert to be held
means
Objective functions :
Maximum profit equation p = 65x +40y
Intersection points :
(10000,10000) (20000,0)(2500,2500)(5000,0)
p at (10000,10000) = 65(10000) + 40(10000) = $1050000
p at (20000,0) = 65(20000) + 40(0) = $1300000
p at (2500,2500) = 65(2500) + 40(2500) = $262500
p at (5000,0) = 65(5000) + 40(0) = $325000
Hence maximum profit occurs when all 20000 reserved seats are sold and the profit is $1300000
Please find attached the graph of it.
