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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

Respuesta :

Answer:

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

raphealnwobi

The Profit function is given by P = 58x - 8500

A linear equation is in the form:

y = mx + b;

where y, x are variable, m is the slope of the line and b is the y intercept.

Let P represent the profit after x units are sold. The linear equation is:

P = mx + b

200 units sold results in $3100 profit. Hence:

3100 = 200x + b   (1)

250 units sold results in $6000 profit. Hence:

6000 = 250x + b    (2)

Solving equation 1 and 2 simultaneously gives m = 58, b = -8500

The Profit function is given by P = 58x - 8500

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