Find the solution to the following problem as a function of a: minimize subject to - x + y 0 ≤x≤a 0≤ y ≤ 1 x² < y

A company that makes and sells baseball caps has found that the total monthly cost C in dollars of producing x caps is given by the function C(x)=0.2x280x+9000. Find the production level that will minimize the monthly cost and find the minimum cost.

Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.