Answer:
The Revenue function is 116x - 4x²
Step-by-step explanation:
Given the Price function, p(x) = 116 - 4x,
Revenue function is given as
R(x) = x.p(x)
= x(116 - 4x)
= 116x - 4x²
...................................
We can even go ahead to determine what the maximum profit would be,
The profit function P(x) is the Revenue function minus the Cost function.
P(x) = R(x) - C(x)
P(x) = (116x - 4x²) - (4x + 8)
= 116x - 4x² - 4x - 8
= 112x - 4x² - 8
P(x) = -4x² + 112x - 8
The Maximum Profit is determined using the value of x at
dP/dx = 0
dP/dx is the first derivative of P(x) with respect to x.
dP/dx = -8x + 112
Max P: -8x + 112 = 0
x = -112/-8 = 14
At dP/dx = 0, the value of x is 14.
Using this in P(x), we obtain the maximum profit
P(14) = -4(14²) + 112(14) - 8
= 776
the expression for revenue function R(x) = 116x-4x²
Revenue function is the product of the number of units and the demand price per unit.
it is given that,
cost to produce 'x' designer leashes = 4x+8
price demand function per leash = 116-4x
as we know,
revenue function = total number of units* demand function
revenue function = x(116-4x)
revenue function = 116x-4x²
hence, revenue function R(x) = 116x-4x²
to get more about revenue function refer to the link,
https://brainly.com/question/19755858
