All are welcome to answer, but only an answer with ALL WORK SHOWN will receive L

Question

All are welcome to answer, but only an answer with ALL WORK SHOWN will receive LIFESAVER rating.

(Prefer if you can upload picture of work ... but if you can show here that is fine as well)

Carl jogs, plays handball, and swims at the athletic club. Jogging uses 15 calories per minute, handball 11, and swimming 7. He swims 30 minutes and plays handball at least twice as long as he jogs.

If he has 90 minutes to exercise, how long should he participate in each activity to maximize calories used?

Must set up linear programming problem and define all variables...

Explanation / Answer

time for jog=t1 time for handball=t2 time for swim=t3 t1+t2+t3=90 maximize Z= 15t1+11t2+7t3 taking t1=30 min timeleft=90-30=60 min constraints t2+t3=60 t2=2t3 3t3=60 t3=20 t2=40 Z= 15t1+11t2+7t3=15*30+11*40+7*20=450+440+140 =1030 cal

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