number of mice and rats that can be used in the experiment? How many mico and how many rats produce this maximum? \begin{tabular}{|c|c|c|c|} \hline & \multicolumn{2}{|c|}{ Tlme } & \multirow{2}{*}{\begin{tabular}{l} Maximum Time \\ Avallable per Day \end{tabular}} \\ \hline & Mice & Rats & \\ \hline Box A & $20 \mathrm{~min}$ & $10 \mathrm{~min}$ & $840 \mathrm{~min}$ \\ \hline Box B & $10 \mathrm{~min}$ & $20 \mathrm{~min}$ & $720 \mathrm{~min}$ \\ \hline \end{tabular} What is the maximum number of mice and rats that can be used in the experiment? alculator Ask my instructor Clear all Checkanswer

Step 1 ：This problem can be solved using linear programming. The goal is to maximize the number of mice and rats used in the experiment, subject to the constraints given by the time available in each box.

Step 2 ：The constraints can be represented as follows: The time spent on mice in Box A and Box B should not exceed the total time available in each box. Similarly, the time spent on rats in Box A and Box B should not exceed the total time available in each box.

Step 3 ：We can represent the number of mice and rats as variables x and y respectively. The objective function to maximize would then be x + y.

Step 4 ：The constraints can be represented as follows: \(20x + 10y \leq 840\) (Box A) and \(10x + 20y \leq 720\) (Box B).

Step 5 ：Solving this system of inequalities, we find that the optimal solution is to use 32 mice and 20 rats in the experiment. This is the maximum number of mice and rats that can be used in the experiment given the constraints on the time available in each box.

Step 6 ：Final Answer: The maximum number of mice that can be used in the experiment is \(\boxed{32}\) and the maximum number of rats that can be used is \(\boxed{20}\).