Answer
a. Plan-A, $y_1=4+0.1x$ , Plan-B, $y_2=2+0.15x$
b. See graph
c. $41$ or more checks.
d. See explanations.
Work Step by Step
a. For Plan-A, we have $cost1=y_1=4+0.1x$ and for Plan-B, we have $cost2=y_2=2+0.15x$
b. See graph, red line for $y_1$ and blue line for $y_2$.
c. For Plan-A to be better than Plan-B, we need $cost1\lt cost2$ and $y_1\lt y_2$. The intersect point can be found at $(40,8)$, thus the solution is $x\gt 40$ or the interval of $(40,\infty)$ which means $41$ or more checks (integers).
d. To solve $y_1\lt y_2$, we have $4+0.1x\lt 2+0.15x$ which gives $2\lt 0.05x$ and $40\lt x$ or $x\gt 40$ which confirms the above result.
