Expert: Richard J. Raridon - 10/23/2006

Question
I have some questions that are based on the following information.  I would appreciate your answers very much, thank you.

A psychology department buys mice and rats for experiments.  They have cages for at most 300 mice and rats.  Each mouse costs $1 to purchase and each rat costs $2 to purchase.  The department has a total of $400 available to purchase the animals.  Each mouse can be used for 73 experiments and each rat can be used for 111 experiments.  How many mice and rats should be bought in order to maximize the number of experiments that can be performed?

1. identify and graph the following.

A.The inequality which expresses the limitation for the number of cages they have to house animals.
b.The inequality which expresses the limitation for the amount of money they have to spend purchasing the mice and rats.
c. Identify the objective function that will be used to maximize the number of experiments they can perform.

Answer
a. C <= 300
b. A(mount) <= 400
If you optimize the number of cages used and the amount of money available, you have M+R = 300 and M+2R = 400
so M = 200 and R = 100
which looks like it gives the optimum no. of experiments,
E = 73M +111R = 25700