Final answer:
The marginal revenue at the sale of 6000 picnic tables is determined by differentiating the revenue function and then plugging in the value 6000 into the obtained marginal revenue function. The calculation shows that the marginal revenue at this quantity is $17 per table.
Step-by-step explanation:
The student is asking to find the marginal revenue at the sale of 6000 picnic tables using the given revenue function R(x) = 41x - x²/500. Marginal revenue is the derivative of the total revenue function with respect to the number of units sold, which represents the additional revenue generated from the sale of one more unit.
To find the marginal revenue function, MR(x), we differentiate R(x) with respect to x. The derivative of 41x with respect to x is 41, and the derivative of -x²/500 with respect to x is -x/250. So the marginal revenue function is MR(x) = 41 - x/250.
Plugging in x = 6000 into the marginal revenue function provides the marginal revenue when 6000 tables are sold. The calculation step is as follows:
MR(6000) = 41 - 6000/250
= 41 - 24
= 17
Therefore, the marginal revenue when 6000 tables are sold is $17 per table.