Consider the linear program max 10y1 + y2 s.t. 3y1 + 2y2 6 2y1 + 4y2 8 y1, y2 0 (a) Solve

Consider the linear program max 10y1 + y2 s.t. 3y1 + 2y2 Ú 6 2y1 + 4y2 … 8 y1, y2 Ú 0

(a) Solve the problem graphically. Be sure to identify all constraints, show contours of the objective, outline the feasible space, and justify that an optimal solution is y1 * = 4, y2 * = 0.

(b) Place the above LP in standard form using nonnegative slack variables y3 and y4.

(c) Explain why a main constraint in the original model will be active at a given solution exactly when the corresponding solution in standard form has its slack’s nonnegativity constraint active at value = 0.