ABSTRACT
In this chapter, the authors discuss problems like the pumping station location that they can model and solve using single-variable calculus. They review the calculus concepts needed for optimization, and then apply them to applications. Bell Computers spends $ 250 in variable costs to produce an SP6 computer. They have a fixed cost of $ 5500 whenever the plant is in operation and computers are produced. In numerical methods of optimization, a procedure is used in obtaining values of the objective function at various combinations of the decision variables, and conclusions are then drawn regarding the optimal solution. Newton’s Method can be adapted to solve nonlinear optimization problems. For a twice differentiable function of one variable, the adaptation is straightforward. In order to use the modified Newton’s Method to find critical points, the function’s first and second derivatives must exist throughout the neighborhood of interest.
