A company charting its profits notices that the relationship between the number of units sold, x, and the profit, P, is linear. If 200 units sold results in $3100 profit and 250 units sold results in $6000 profit, write the profit function for this company

P = 58x - 8500

Step-by-step explanation:

Given;

If 200 units sold results in $3100 profit and 250 units sold results in $6000 profit

The linear form of the profit function can be written as;

P = mx + c ... a

Where;

P = profit

x = number of units sold

m = slope

c = intercept

Substituting the given values, we can derive two equations;

3100 = 200m + c ... 1

6000 = 250m + c ... 2

Subtracting equation 1 from 2

2900 = 50m

m = 2900/50

m = 58

Substituting m = 58 into equation 1;

3100 = 200 (58) + c

c = 3100 - 200 (58)

c = - 8500

Substituting m and c into the equation a.

Therefore, the profit function of the company is;

P = 58x - 8500