Question

An experiment involves placing the males and females of a laboratory animal species in two separate controlled environments. there is a limited time available in these environments, and the experimenter wants to maximise the number of animals subject to the constraints described. how many males and how many females will maximise the total number of animals? males females time available environment a 20 min 25 min 800 min environment b 20 min 15 min 600 min

Answer 1

15 males and 20 females would maximize the total number of animals

How to determine the number of males and females?

The table is given as:

                           Males      Females    Time available

Environment a    20 min      25 min       800 min

Environment b    20 min      15 min       600 min

Represent the male with x and the female with y.

The time available is limited i.e. ≤

So, the constraints are:

20x + 25y ≤ 800

20x + 15y ≤ 600

Solve the above system of inequalities graphically (see attachment)

(x, y) = (15,20)

Hence, 15 males and 20 females would maximize the total number of animals

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