Question

A company charting its profits notices that the relationship between the number of units sold, x, and the profit, P, is linear. If 170 units sold results in $1360 profit and 220 units sold results in $4260 profit, write the profit function for this company.

Answer 1

Answer:

P(x) = 58x - 8,500

Step-by-step explanation:

The profit function can be modeled based on the two given points of format (P, x) that are ($1360, 170) and ($4260, 220). The slope of the function is:

$m=\frac{4,260-1,360}{220-170}\\ m=58$

Applying the general form of a linear equation, the profit function is:

$P-P_0 = m*(x-x_0)\\P - 1,360=58*(x-170)\\P(x) = 58x -8,500$

The profit as a function of units sold is P(x) = 58x - 8,500.