The quantity of Sensitech laser gaming mice demanded each month is related to the unit price by the equation
p = 42/0.03x^2 + 1 (0 ≤ x ≤ 20)
Find the revenue function R.
Find the marginal revenue function R'.
R = p x = 42/0.03x + x = 1400 /x + x
dR/dx = -1400 /x^2 + 1
To find the revenue function R, we need to multiply the unit price (p) by the quantity (x) demanded each month. So, the revenue function R can be expressed as:
R = p * x
Substituting the equation of p into the revenue function, we get:
R = (42/0.03x^2 + 1) * x
Simplifying this expression, we have:
R = (42/0.03)x^3 + x
Therefore, the revenue function R is given by:
R = (42/0.03)x^3 + x
Now, let's find the marginal revenue function R'.
To find the marginal revenue function R', we need to differentiate the revenue function R with respect to x. In other words, we need to find the derivative of R with respect to x.
Differentiating the revenue function R = (42/0.03)x^3 + x, we get:
R' = (3 * (42/0.03))x^2 + 1
Simplifying this expression, we have:
R' = 1260x^2 + 1
Therefore, the marginal revenue function R' is given by:
R' = 1260x^2 + 1