A manufacturer's revuenve in dollars is given by R(x)=1500x-0.02x^2 where x is number of units sold.
Find the marginal revenue function. Use the derivative to estimate the revenue gained from selling the 35th unit.
The marginal revenue function is the derivative, dR/dx = 1500 - 0.04 x.
Insert x = 35 for the revenue gain by selling the 35th unit. It is still pretty close to $1500.
To find the marginal revenue function, we need to take the derivative of the revenue function, R(x), with respect to x, which represents the number of units sold.
R(x) = 1500x - 0.02x^2
To find the derivative, we differentiate each term of the function with respect to x.
The derivative of 1500x with respect to x is 1500.
The derivative of -0.02x^2 with respect to x can be found using the power rule. The power rule states that for any term of the form ax^n, where a is a constant and n is a real number, the derivative with respect to x is given by nx^(n-1).
Using the power rule, the derivative of -0.02x^2 with respect to x is -0.02 * 2x^(2-1) = -0.04x.
Therefore, the marginal revenue function, expressed as the derivative of R(x), is:
dR/dx = 1500 - 0.04x
Now, to estimate the revenue gained from selling the 35th unit, we substitute x = 35 into the marginal revenue function, dR/dx.
dR/dx = 1500 - 0.04(35)
= 1500 - 1.4
= 1498.6
Therefore, the estimated revenue gained from selling the 35th unit is approximately $1498.6.