Optimization Calculus

Question

1.A piece of cardboard measuring 12 inches by 10 inches is formed into an open-top box by cutting squares with side length  from each corner and folding up the sides.

Find a formula for the volume of the box in terms of X.

Find the value for  that will maximize the volume of the box

2.A rectangular storage area is to be constructed along a side of a building. A security fence is required along the remaining three sides of the area. What is the maximum area that can be enclosed with 985 ft of fencing?

Length of the side parallel to the building is

Length of the side perpendicular to the building is

The maximum area of the storage area is 

3.You are a lifeguard and spot a drowning child 60 meters along the shore and 70 meters from the shore to the child. You run along the shore and for a while and then jump into the water and swim from there directly to child. You can run at a rate of 3 meters per second and swim at a rate of 1.1 meters per second. How far along the shore should you run before jumping into the water in order to save the child? Round your answer to three decimal places.

Answer 1

These are optimization questions and are simple once u understand the concept. It is difficult to draw a digram and explain in a text window. Do u want to do a quick online session for me to explain?