Consider the following linear programming problem:
Max 50x_1+ 34_2
s.t. 10x_1 + 7x_2 ≤ 49
x_1+ x_2 ≥ 5
x_1, x2 ≥ 0
a. Write the problem in standard form. Identify slack/surplus variables.
b. Identify the feasible region and find the optimal solution.
c. What are the values of the slack and surplus variables at the optimal solution?