The average cost function, a(x), is defined as a(x) = c(x)/x, where c(x) is the cost function and x is the number of units produced. Find the production level to minimize the average cost if:

c(x)=25000+100x+4x^3/2

A sports complex is to be built in the form of a rectangular field with 2 equal semicircular areas at each end. If the border of the entire complex is to be a running track 400 m long, what should the dimensions of the complex be so that the area of the rectangular field is maximized?[Include diagram]

We want to build a box whose base length is 6 times the base width and the box will enclose 20 in^3. The cost of the material of the sides is $3 per in^2 and the cost of the top and bottom is $15 per in^2. Determine the dimensions of the box that will minimize the cost needed to construct the box. [Include Diagram]