Maximize and minimize p = 2x − y subject to x + y ≥ 1 x − y ≤ 1
x − y ≥ −1 x ≤ 7, y ≤ 7.
Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT (See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = 8x - By subject to 7 sy ys 2x x + y27 x + 2y = 16 x>0, y 2 0. c= (x,y) = ((
Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) a)Maximize p = 3x + 2y subject to −4x+y≥10 x+3y≤12 x ≥ 0, y ≥ 0 p= (x,y)= b) Maximize and minimize p = x + 2y subject to x + y ≥ 6 x + y ≤ 8 x...
Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = x + y subject to x + 5y ≥ 6 5x + y ≥ 6 x ≥ 0, y ≥ 0. c = x = y =
Maximize P = 4x + 5y subject to 2x + y < 50 2 + 3y < 75 2 > 0 y > 0 Identify the feasible region as bounded or unbounded: List the corner points of the feasible region, separated by a comma and a space. If the region is unbounded, create appropriate ghost points and list those as well. For each corner point, list the value of the objective function at that point. The format should be (x1,y1)...
Solve the given linear programming problem using the simplex method. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the feasible region is empty and UNBOUNDED if the objective function is unbounded.) Minimize c = x + y + z + w subject to x + y ≥ 80 x + z ≥ 60 x + y − w ≤ 50 y + z − w ≤ 50...
5. Waner p 302 #1) Given the LP problem: Maximize p = 2x + y subject to: Constraint 1: x + 2y <= 6 Constraint 2: -x + y<=4 Constraint 3: x + y = 4 XX. >= 0 The final simplex tableau is as follows: Basic 10 0 Answer the following questions: Find the new value of the objective function when b3 is changed from 4 to 6. g) The range of values of 4 (63) such that the...
Consider the following constraints and the c g graph below: Constraint L:4x-y21 Constraint 2: x+ys4 Constraint 3:-x-4y 2-8 x, y20 4x-y=1 x-4y -8 a. (2 points) Shade the feasible region in the graph provided above. b. (1 point) For this part only the objective function is Minimize -2x + y. Which of the following describes the optimal solution? (Put a check next to your answer) Infeasible solution Unique optimal solution the point (4,0) minimizes the LP Alternate optimal solution Unbounded...
Explain why the linear programming problem has no optimal solution Maximize P = 2X7 + 8x2 subject to 3x4 - 5x2 5 15 X, X₂20 Choose the correct answer below O A. The feasible region for the problem is unbounded, because every point with coordinates (x,x), where x, 20 and X 20, satisfies the problem const O B. The feasible region for the problem is unbounded, because every point with coordinates (0x2), where x2 2 0, satisfies the problem constraint...
Solve the linear programming problem. Minimize and maximize z=50x+10y Subject to 2x+y ≥ 32 x+y ≥ 24 x+2y ≥ 28 x, y ≥ 0
4. Given the following linear programming problem, determine which situation (choose one) a. An optimal solution exists at a single vertex point. b. There is more than one optimal solution. C. There is no optimal solution because the feasible region does not exist d. There is no optimal solution because the feasible region is unbounded. Maximize: 2x +3y Subject to: x +2y 28 5. Graph the inequality: 2x +3y >12 6. Graph the system of inequalities: 7. Graph the system...