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    John is reviewing his lifestyle, and in particular his leisure commitments. He enjoys badminton and squash, but is not sure whether he should persist with one or both. Both cost money and both take
    time.

    Playing badminton costs £3 per hour and playing squash costs £4 per hour. John has £11 per week to spend on these activities.

    John takes 0.5 hours to recover from every hour of badminton and 0.75 hours to recover from every hour of squash. He has 5 hours in total available per week to play and recover.

    (i) Define appropriate variables and formulate two inequalities to model John’s constraints. [3]

    Answer

    I got the first constraint:

    3x + 4y ≤ 11

    But, im not sure how to work the other one out.

    The mark scheme says 1.5x + 1.75y ≤ 5

    How do you work this one out??
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    Playing badminton costs £3 per hour and playing squash costs £4 per hour. John has £11 per week to spend on these activities.

    3x+4y≤11

    1x+0.5x+1y+0.75y≤5 ---> 1.5x + 1.75y ≤ 5
    Just use all the information, for every hour he plays badminton (1x) he needs 0.5 hours to recover (0.5x), 1 hour of squash (1y) he needs 0.75 hours to recover (0.75y) and this all must be less than 5 hours in total.

    Just got to get your head round it, keep trying more linear programming questions.
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    kool,

    thnx
 
 
 
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