Answer: 3 hours for him to break even
Step-by-step explanation:
(if this helps, do you mind giving brainlyist?)
To find the number of hours it takes for JD to break even, we need to set the revenue equal to the overhead cost and solve for h.
The revenue function R(h) is given by R(h) = 3h + 7, and the overhead cost function C(h) is given by C(h) = h² + 7h - 14.
To find the break-even point, we set R(h) equal to C(h) and solve for h:
3h + 7 = h² + 7h - 14
Rearranging the equation, we get:
0 = h² + 7h - 3h - 14 - 7
0 = h² + 4h - 21
Now, we can factor the quadratic equation:
0 = (h - 3)(h + 7)
Setting each factor equal to zero, we have:
h - 3 = 0 or h + 7 = 0
Solving for h, we get:
h = 3 or h = -7
Since we are dealing with hours worked, the number of hours cannot be negative. Therefore, we discard the solution h = -7.
Thus, JD breaks even after 3 hours of work.
In summary, JD breaks even after working for 3 hours.
