A factory is building a 500-square feet open rectangular cooling pool for water exhausted from its main process. The pool will be 8 feet deep, its length should be at least twice its width, and there is room for a width of at most 15 feet. We wish to choose the feasible design that minimizes cost by minimizing the concrete area of the pool walls.

(a) Formulate a mathematical programming model with 3 main constraints to choose an optimal design using decision variables x1! length of the pool and x2! width of the pool.

(b) Enter and solve your model with the class optimization software.

(c) Using a 2-dimensional plot, solve your model graphically for an optimal design.

(d) On a separate 2-dimensional plot, show graphically that the problem becomes infeasible if the pool can be at most 25 feet in length.