Chapter 6.2, Problem 30E

In Problems 33 and 34, first solve the linear programming problem by the simplex method, keeping track of the basic feasible solutions at each step. Then graph the feasible region and illustrate the path to the optimal solution determined by the simplex method.

$\begin{array}{l}\text{Maximize }P=5x_1+3x_2\\ \text{subject to 5}{x}_1+4x_2\le 100\\ \text{ 2}{x}_1+x_2\le 28\\ \text{ 4}{x}_1+x_2\le 42\\ x_1\le 10\\ x_1,x_2\ge 0\end{array}$