Calculus - Optimization

Q1

You wish to fence in a rectangular pasturing area which will be subdivided into two smaller rectangles by an extra fence parallel to one pair of sides. You have 24002400meters of fencing to use for your whole project. What dimensions for your pasture will maximize its area?

Q2

Find the point on the line =5+2y=5x+2 which is closest to the origin.

Q3

A rectangular storage container with an open top is to have a volume of 1010 cubic meters. The length of its base is twice its width. Material for the base costs 55 dollars per square meter and material for the sides of the container costs 33 dollars per square meter. Find the lowest possible cost of materials for the container.

Q4

Find two positive numbers whose product is 225 and whose sum is as small as possible.

Q5

Find the point on the graph of ()=82f(x)=82x which is closest to the point (2,0)(2,0).