8.4 Inequalities Of Combined Functions

Your group has just won a dragon boat race and your prize is the last 10 pandas in the world. To celebrate, you row to the middle of the Yellow Sea and have some lunch.

All good things come to an end, however, as you have just received a tweet that there is a bomb taped to the underside of your dragon boat and the nearest help is 40 minutes away.

Unfortunately, the chicken fried rice you had for lunch has now made you bloated and nobody can swim underneath the boat to stop the bomb from going off. 

The bomb will blow up in 5 minutes and the hole it creates will let in 1.7 tonnes of water per minute. Your boat can take 30 tonnes of water before it sinks, drowning you and the pandas. 

You can try to keep your boat afloat until help arrives by pumping water overboard, but one person can only pump 4.5log(t+1) tonnes of water, with t representing the number of minutes the person pumps.  You can also try to move as many pandas as you can to the bamboo life rafts, but it takes 10 minutes for one person to move one panda to the life rafts (note: only one person can move one panda at a time).  

YOUR MISSION:

Figure out what each person must do after the bomb explodes, in order to save as many pandas as possible.

Answer

1 pumping 3 moving pandas: 6 pandas saved2 pumping 2 moving pandas: 4 pandas saved3 pumping 1 moving pandas: 2 pandas saved

everyone moving the pandas: 4 pandas saved everyone pumping: you & all the pandas died

the end.