The average ticket price for a concert at the opera house was $40. The average attendance was 1500. When the ticket price was raised to $44, attendance declined to an average of 1100 persons per performance. What should the ticket price be to maximize revenue for the opera house?

price should decease by 31% to $27.60 per ticket and total revenue = $75,6666.78

Step-by-step explanation:

total revenue at original price = $40 x 1500 = $60,000

the price elasticity of demand = [(1100 - 1500) / 1500] / [($44 - $40) / $40] = -26.7% / 10% = -2.67 or |2.67| in absolute terms which means that the demand is very elastic.

since the PED is very elastic, the price should decrease

If price decreases by 10%, attendance will increase by 26.7%, so total revenue = $36 x (1500 x 1.267) = $36 x 1900 = $68,400

If price decreases by 20%, attendance will increase by 53.4%, so total revenue = $32 x (1500 x 1.534) = $32 x 2301 = $73,632

If price decreases by 30%, attendance will increase by 80.1%, so total revenue = $28 x (1500 x 1.801) = $28 x 2701 = $75,628

If price decreases by 40%, attendance will increase by 106.8%, so total revenue = $24 x (1500 x 2.068) = $28 x 2701 = $74,448

the price should decrease more than 30%, but less than 40%

If price decreases by 35%, attendance will increase by 93.45%, so total revenue = $26 x (1500 x 1.9345) = $28 x 2902 = $75,452

If price decreases by 33%, attendance will increase by 88.11%, so total revenue = $26.80 x (1500 x 1.8811) = $28 x 2822 = $75,629.60

If price decreases by 32%, attendance will increase by 85.44%, so total revenue = $27.20 x (1500 x 1.8544) = $28 x 2822 = $75,659.52

If price decreases by 31%, attendance will increase by 82.77%, so total revenue = $27.60 x (1500 x 1.8277) = $28 x 2822 = $75,6666.78

slope= 1

y-inter slope= 0

x       y

o     0

1       1

2     2

ect.

step-by-step explanation:

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.