1- There is 120 m of fence to surround a rectangular field. Determine the dimensions that the field must have for its area to be maximum, if it is divided using parallel fences on one side,

A) in three rectangular lots;

2- Determine 2 positive numbers such as

B) their sum is 100 and the square of the first added to the second gives a minimum sum;

3-We want to make a box with a square base, closed on top. The cost of manufacturing the box is $0.03 per cm^2 for the bottom, $0.05 per cm^2 for the top and $0.02 per cm^2 for each side. Determine the dimensions of the box before a maximum volume if its manufacturing cost is $24.