The revenue, in dollars, of a company that makes toy cars can be modeled by the polynomial 3x2 + 4x – 60. the cost, in dollars, of producing the toy cars can be modeled by 3x2 – x + 200. the number of toy cars sold is represented by x.
if the profit is the difference between the revenue and the cost, what expression represents the profit?
3x – 260
3x + 140
5x – 260
5x + 140

For this case we have the following quadratic functions:

Revenue:

Cost:

Then, we observe that the profit is given by the following mathematical relationship:

Substituting values we have:

Making the corresponding calculations we have:

An expression that represents the profit is:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is