Math

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.

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  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

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