John is trying to decide how to divide his time between his job as a stocker in the local grocery store, which pays $7 per hour for as many hours as he chooses to work, and cleaning windows for the businesses downtown. He makes $2 for every window he cleans. John is indifferent between the two tasks, and the number of windows he can clean depends on how many hours he spends cleaning in a day, as shown in the table below: $$\begin{array} { | c | c | }
\hline \begin{array} { c }
\text { Hours Per } \
\text { Day Cleaning } \
\text { Windows }
\end{array} & \begin{array} { c }
\text { Total Number } \
\text { of Windows } \
\text { Cleaned }
\end{array} \
\hline 0 & 0 \
\hline 1 & 7 \
\hline 2 & 11 \
\hline 3 & 14 \
\hline 4 & 16 \
\hline 5 & 17 \
\hline
\end{array}$$ What is the lowest price per window that John would be willing to accept to spend 4 hours per day cleaning windows?

Question

John is trying to decide how to divide his time between his job as a stocker in the local grocery store, which pays $7 per hour for as many hours as he chooses to work, and cleaning windows for the businesses downtown. He makes $2 for every window he cleans. John is indifferent between the two tasks, and the number of windows he can clean depends on how many hours he spends cleaning in a day, as shown in the table below: $$\begin{array} { | c | c | } 
\hline \begin{array} { c } 
\text { Hours Per } \
\text { Day Cleaning } \
\text { Windows }
\end{array} & \begin{array} { c } 
\text { Total Number } \
\text { of Windows } \
\text { Cleaned }
\end{array} \
\hline 0 & 0 \
\hline 1 & 7 \
\hline 2 & 11 \
\hline 3 & 14 \
\hline 4 & 16 \
\hline 5 & 17 \
\hline
\end{array}$$ What is the lowest price per window that John would be willing to accept to spend 4 hours per day cleaning windows?

Quizplus · Accepted Answer

To find the lowest price per window, calculate the opportunity cost of cleaning windows instead of working at the grocery store. In 4 hours, John would earn $28 at the store (4 hours x $7/hour). Cleaning 16 windows in 4 hours, he needs to earn at least $28, so $28/16 windows = $1.75 per window. Since $1.75 is not an option, the closest higher price is $3.50.

John Is Trying to Decide How to Divide His Time