En una institución educativa se va a realizar una función de teatro auditorio tiene una capacidad para 500 asistentes y se fija el precio de la entrada en 10 soles sin embargo debido a gastos adicionales se ven en la necesidad de incrementar el precio sabiendo que por cada un sol de incremento edistirán 10 personas de asistir a dicha función entonces
Answers
Given : 500 people attending event costing ticket 10
Ticket cost increased but increasing cost by 1 will decrease 10 people
To Find : How much cost to be increased to get maximum revenue
% increase in revenue
Solution:
Initial revenue = 500 * 10 = 5000
Let say ticket price increased by x
Then ticket price = 10 + x
Person attending = 500 - 10x
Revenue R(x) = (10 + x)(500 - 10x)
R'(x) = (10 + x)(-10) + ( 1)(500 - 10x)
=> R'(x) = 400 - 20x
R'(x) = 0 => x = 20
R''(x) = - 20 < 0
Hence maximum revenue at x = 20
Ticket price can be increased by 20
Hence ticket price = 10 + 20 = 30
Revenue = 30 * 300 = 9000
Revenue increased by 9000 - 5000 = 4000
increase in revenue % = (4000/5000) * 100 = 80 %
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