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1. The minimization of a function z subject to a set of constraints is equivalent to the maximization of z subject to the same set of constraints. 2. If an LP model has an equality constraint, a slack variable could be added to the constraint and to the objective function. A big penalty M will be assigned to the slack variable in the objective function to forbid it to be greater than 0 . 3. The Simplex method stops when one optimal solution is found but it is possible that other optimal solutions exist. 4. In an LP problem, it is possible to change the right-hand side (resource) without changing the optimal solution. 5. In an LP problem, it is possible to change the coefficients of the objective function without changing the optimal solution. Find the best or the closest answer. You are allowed to use a computer to solve the following problem. Maximize Z=3x1+4x2 Subject to Constraint 1x1+2x25( resource 1) Constraint 2x1+x24( resource 2) x1,x20 6. What is the shadow price for resource I? (a) 0 (c) 2 (d) 3 (e) 4 (f) 5 (g) 6 7. What is the minimally allowed value for resource 1 without changing its shadow price? (a) 0 (b) 1 (c) 2 (d) 3 (c) 4 (f) 5 (g) 6 8. What is the maximally allowed value for resouree 2 without changing its shadow price? (a) 0 (b) 1 (c) 2 (d) 3 (e) 4 (f) 5 (g) 6 9. What is the maximally allowed value for the coefficient of x1 in the objective function without changing the optimal solution? (a) 0 (b) 1 (c) 2 (d) 3 (c) 4 (f) 5 (g) 6 10. What is the minimally allowed value for the coefficient of x2 in the objective function without changing the optimal solution? (a) 0 (b) 1 (c) 2 (d) 3 (c) 4 (f) 5 (g) 6