Mike repairs televisions. His revenue, in dollars, can be modeled by the equation y = 25 + 30x, where x is the number of hours spent repairing televisions. His overhead cost, in dollars, can be modeled by the equation y=5x2−10 , where x is the number of hours spent repairing televisions. After how many hours does he break even? Note: The phrase break even refers to the value where the two functions are equivalent.
Answer: At x = 7 hours spent on repairing television he will get break even point.
Step-by-step explanation:
Since we have given that
Equation of revenue is given by
\(y=25+30x\)
where x is the number of hours spent repairing television.
Equation of overhead cost is given by
\(y=5x^2-10\)
We need to find the break even point.
As we know the break even situation:
\(R(x)=C(x)\\\\25+30x=5x^2-10\\\\5x^2-10-25-30x=0\\\\5x^2-30x-35=0\\\\x^2-6x-7=0\\\\x^2-7x+x-7=0\\\\x(x-7)+1(x-7)=0\\\\(x+1)(x-7)=0\\\\x=-1,7\\\\x=7\)
Hence, at x = 7 hours spent on repairing television he will get break even point.