A firm has total revenue given by dollars for x units of a product. Find the maximum revenue from sales of that product.

Question

A firm has total revenue given by  dollars for x units of a product. Find the maximum revenue from sales of that product. ​

Quizplus · Accepted Answer

To find the maximum revenue, we need to find the maximum value of the revenue function. We can do this by taking the derivative of the revenue function with respect to x and setting it equal to zero. 
The derivative of the revenue function is 11eb0d3b_9868_0f84_9790_5bed029bc3b5_TB1243_11 * e^(0.693x). 
Setting this equal to zero and solving for x, we get x = -ln(2)/0.693 ≈ 1.59. 
To confirm that this is a maximum, we can take the second derivative of the revenue function with respect to x. The second derivative is 11eb0d3b_9868_0f84_9790_5bed029bc3b5_TB1243_11 * e^(0.693x)*0.693, which is always positive. Therefore, x = 1.59 corresponds to a maximum revenue. 
Plugging this value into the revenue function, we get 11eb0d3b_9868_0f86_9790_5b8ba5156ca1_TB1243_11 dollars as the maximum revenue.

A Firm Has Total Revenue Given by Dollars for X