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September 13th, 2017, 01:59 PM   #1
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Linear Programming Problem!

The semester has just started and you want to come up with an optimal daily schedule for your off-class time, i.e. you want to know the time you need to allocate to studying, and the time you need to allocate for extra- curricular activities. For a more balanced life, you want to ensure that the time allocated to studying is at least 20% of your time, and the time for extra-curriculars is at least 20% of your time. Furthermore, you cannot allocate more than 3 hours to any of those two. If the maximum amount of time you can spend daily is 5 hours, and you believe that studying is 1.5 times more beneficial to you than extracurriculars, find the daily schedule that maximizes your benefit.

I really only need the constraints, but if you want to answer the whole thing feel free (: thank you!
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September 13th, 2017, 02:45 PM   #2
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total time is $T=5hr$

$T_{study} \geq (0.2)T = 1hr$

$T_{ec} \geq (0.2)T = 1hr$

$1 \leq T_{study} \leq 3$

$1 \leq T_{ec} \leq 3$

$benefit = (1.5)T_{study} + T_{ec}$

It seems pretty clear that you want to maximize the study time subject to the constraint that you spend at least an hour on extra-curricular activities.

However the other constraint kicks in and you can only spend a maximum of $3hr$ studying.

So just by inspection the optimal solution is $T_{study}=3,~T_{ec}=2$
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