A company charting its profits notices that the relationship between the number of units sold x and the profit P is linear. If 800 units sold results in $3533 profit and 875 units sold results in $8483 profit, find the marginal profit, which is the rate of change of the profit.

Question

A company charting its profits notices that the relationship between the number of units sold x and the profit P is linear. If 800 units sold results in ​$3533 profit and 875 units sold results in ​$8483 ​profit, find the marginal​ profit, which is the rate of change of the profit.

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GPT-4o mini · Answer

To find the marginal profit, which is the rate of change of profit with respect to the number of units sold, we need to determine the slope of the line represented by the two points given: (800, 3533) and (875, 8483).

The formula for the slope (m) of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

In this case, let:

$(x_1, y_1) = (800, 3533)$
$(x_2, y_2) = (875, 8483)$

Now, we can substitute these values into the formula:

\[ m = \frac{8483 - 3533}{875 - 800} \]

Calculating the changes in profit and units sold:

\[ m = \frac{4950}{75} \]

Now, performing the division:

\[ m = 66 \]

Thus, the marginal profit, or the rate of change of profit with respect to the number of units sold, is $66 per unit.

A company charting its profits notices that the relationship between the number of units sold x and the profit P is linear. If 800 units sold results in ​$3533 profit and 875 units sold results in ​$8483 ​profit, find the marginal​ profit, which is the rate of change of the profit.

A company charting its profits notices that the relationship between the number of units sold x and the profit P is linear. If 800 units sold results in $3533 profit and 875 units sold results in $8483 profit, find the marginal profit, which is the rate of change of the profit.