The profit obtained when x barbecues are sold is
P(x) = 100 x − 3x^2 (lnx) dollars . Find the marginal profit when 4 are sold.
P(4) =
100(4) - 3(16)ln(4)
= ..
I assume you have a calculator to get appr 333.46
the marginal profit is
dP/dx = 100 - 6x lnx - 3x
so, now plug in x=4
To find the marginal profit when 4 barbecues are sold, we need to find the derivative of the profit function with respect to the number of barbecues sold, and then evaluate it at x = 4.
Step 1: Find the derivative of the profit function P(x) with respect to x.
P(x) = 100x - 3x^2ln(x)
To find the derivative, we can use the product rule and the chain rule.
dP/dx = 100 - (6xln(x) + 3x)
Simplifying further, we get:
dP/dx = -6xln(x) - 3x + 100
Step 2: Evaluate the derivative at x = 4.
dP/dx = -6(4)ln(4) - 3(4) + 100
= -24ln(4) - 12 + 100
= -24ln(4) + 88
Therefore, the marginal profit when 4 barbecues are sold is -24ln(4) + 88 dollars.