Question

The revenue in dollars generated from a sale of x picnic tables is given by R(x) = 38x - (x²)/100.

Answer parts (a) through (d)

(a) Find the marginal revenue when 1000 tables are sold.

Answer 1

To find the marginal revenue when 1000 tables are sold, take the derivative of the revenue function. The marginal revenue is 58 dollars.

Step-by-step explanation:

To find the marginal revenue when 1000 tables are sold, we need to take the derivative of the revenue function with respect to x. The revenue function is given by R(x) = 38x - (x²)/100. Taking the derivative of this function gives us the marginal revenue function, which represents the rate of change of revenue with respect to the number of tables sold.

Using the power rule, we can differentiate 38x and (x²)/100 separately. The derivative of 38x is 38, and the derivative of (x²)/100 is (2x)/100. Adding these derivatives together gives us the marginal revenue function: MR(x) = 38 + (2x)/100.

Substituting x = 1000 into the marginal revenue function gives us MR(1000) = 38 + (2(1000))/100 = 38 + 20 = 58 dollars.