Answer:
The daily revenue equation is 29700 - 90x - 30x²
The price that should be charged to maximize daily revenue is $15.75
Step-by-step explanation:
Revenue is a function of price multiplied by the quantity. Thus, the equation for revenue can be written as,
Let x be the number of times there is an increase in price of $0.5.
The price function is = 16.5 + 0.5x
The demand function is = 1800 - 60x
Revenue = (16.5 + 0.5x) * (1800 - 60x)
Revenue = 29700 - 990x + 900x - 30x²
Revenue = 29700 - 90x - 30x²
To calculate the price that will yield maximum revenue, we need to take the derivative of this equation of revenue.
d/dx = 0 - 1 * 90x° - 2 * 30x
0 = -90 -60x
90 = -60x
90 / -60 = x
x = -1.5
The price needed to maximize revenue is,
p = 16.5 + 0.5 * (-1.5)
p = 16.5 - 0.75
p = 15.75
The demand at this price is = 1800 - 60 * (-1.5)
Demand = 1800 + 90 = 1890