The problem states that the relationship between the number of units sold $x$ and profit $P$ is linear. Given that 190 units sold results in $1380 profit, and 240 units sold results in $3980 profit, we need to find the marginal profit. The profit function is already given as $P = 52x - 8500$.

1. Problem Description

The problem states that the relationship between the number of units sold $x$ and profit $P$ is linear. Given that 190 units sold results in $1380 profit, and 240 units sold results in$3980 profit, we need to find the marginal profit. The profit function is already given as $P = 52x - 8500$.

2. Solution Steps

Since the relationship between $x$ and $P$ is linear, the marginal profit is the slope of the linear equation relating profit $P$ to the number of units sold $x$. The profit function is given by $P = 52x - 8500$.

The slope of this equation is the coefficient of $x$, which is

5

2. Alternatively, the marginal profit can be found using the two points given: (190, 1380) and (240, 3980).

Marginal profit = (Change in profit) / (Change in units sold).

Marginal profit = $\frac{3980 - 1380}{240 - 190} = \frac{2600}{50} = 52$.

The marginal profit is the increase in profit for each additional unit sold. Since $P = 52x - 8500$, for each unit increase in $x$, the profit increases by

5

2. Thus the marginal profit is $

5

2.

3. Final Answer

$52