Question

An experiment involving learning in animals requires placing white mice and rabbits into separate, controlled environments, environment I and environment II. The maximum amount of time available in environment I is 500 minutes, and the maximum amour of time available in environment II is 600 minutes. The white mice must spend 10 minutes in environment I and 25 minutes in environment II, and the rabbits must spend 15 minutes in environment I and 15 minutes in environment II. Find the maximum possible number of animals that can be used in the experiment, and find the number of white mice and the number of rabbits that can be used.

Answer 1

working all those words into numbers, we have

maximize m+r subject to
10m + 15r <= 500
25m + 15r <= 600

I see that we have 15m <= 100
so m <= 6

Given that, if we choose only 1 mouse, we have
15r <= 490
15r <= 575
so, r <= 32

max achieved at 6 mice and 29 rabbits

Answer 2

Aubrey and Charlie are driving to a city that is 120 mi from their house. They have already traveled 20 mi, and they are driving at a constant rate of 50 mi/h. Complete the function that models the distance they drive as a function of time. Then complete a reasonable domain for this situation.