Question

Suppose the revenue (in dollars) from the sale of x units of a product is given by R(x)=2x+274x2+79x​ Find the marainal revenue when 57 units are sold. (Round your answer to the nearest dollar.) 5 Interpret your result. When 57 units are sold, the projected revenue from the sat of unit 58 would be $

Answer 1

The marginal revenue when 57 units are sold is $31,255. This means that for every additional unit sold beyond the 57th unit, the revenue will increase by approximately $31,255.

Step-by-step explanation:

The revenue (in dollars) from the sale of x units of a product is given by R(x)=2x+274x^2+79x.

To find the marginal revenue when 57 units are sold, we first take the derivative of the revenue function:

R'(x) = 2 + 548x + 79

Next, we substitute x = 57 into the derivative:

R'(57) = 2 + 548(57) + 79

Simplifying the expression:

R'(57) = 31255

Therefore, the marginal revenue when 57 units are sold is $31,255.

The result indicates that for every additional unit sold beyond the 57th unit, the revenue will increase by approximately $31,255.