Abox with a square base and open top is to have a volume of 72000 cubic inches. the material for the base costs 4 cents per square inch, while the material for the sides costs 6 cents per square inch. find the dimensions which minimize the cost of material.

It is saturday morning and jeremy has discovered he has a leak coming from the water heater in his attic. since plumbers charge extra to come out on the weekends, jeremy is planning to use buckets to catch the dripping water. he places a bucket under the drip and steps outside to walk the dog. in half an hour the bucket is 1/5 of the way full. what is the rate at which the water is leaking per hour?