## Optimisation!

Hey guys, sorry Im in a hurry, so if I make mistakes while typing, my bad.

1)
A SWAT team member is attempting to exit a warehouse via
a ventilation shaft that is at the top of a wall, level with the
roof. The roof is 30m high and she is currently on the floor,
a distance of 40m from the wall. She can use a crossbow to
attach a rope to the roof, climb the rope and then work her
way along a roof beam to the shaft. She can climb the rope
at 1m/s and can move along the roof beam at 2m/s. What is
the quickest she can reach the shaft?

x = 10(sqrt(3)) m

Total time taken = 20 + 15(sqrt(3)) which approximately equals 45.98 seconds.

Am I right?

2)
A sheet of cardboard 30cm by 40cm is to be cut into a box with a lid, as
shown below.

Find the dimensions of the box that maximise the volume it contains.

x = 5.657cm
so
H = 5.657cm
W = 14.343 cm
L = 18.685 cm

All of the dimensions are approx of course. So am I right.

Sorry Im just checking that Ive done these questions right as Ive got a mid semester exam coming!!!

3) Last question. Its to do with maxima and minima and critical points.

Can a point on a graph be an absolute AND relative maximum/minimum at the same time? Or is a point a absolute maximum/minimum OR a relative maximum/minimum?