The problem states that the relationship between the number of units sold, $x$, and the profit, $P$, is linear. We are given two data points: 190 units sold results in $1380 profit, and 240 units sold results in $3980 profit. We are asked to find the marginal profit. The problem already provides the profit function $P=52x - 8500$ and the marginal profit is asked.

1. Problem Description

The problem states that the relationship between the number of units sold, $x$, and the profit, $P$, is linear. We are given two data points: 190 units sold results in $1380 profit, and 240 units sold results in$3980 profit. We are asked to find the marginal profit. The problem already provides the profit function $P=52x - 8500$ and the marginal profit is asked.

2. Solution Steps

The profit function is given as $P = 52x - 8500$. The marginal profit is the derivative of the profit function with respect to the number of units sold, $x$. In this case, the profit function is linear, so the marginal profit is simply the coefficient of $x$.

$P(x) = 52x - 8500$

The derivative of $P(x)$ with respect to $x$ is:

$\frac{dP}{dx} = 52$

The marginal profit is $

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3. Final Answer

$52