Consider the following constraints and the corresponding graph below: Constraint 1 Constraint 2:x+2ys8 Constraint 3 x-3y...
Consider the following constraints and the corresponding graph below Constraint 1: 2x-y21 Constraint 2:x+2y S8 Constraint 3: x-3y 2-2 2x-y-1 4 x +2y 8 4 7 a. (3 points) Shade the feasible region in the graph provided above. b. (3 points) The objective function is Minimize 2x-3y. Mark the optimal solution(s) in the above graph Do not calculate the x and y coordinates at optimal solution(s). Draw the optimal objective function line through the optimal solution(s).
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...
The graphs show the constraint and several level curves of the objective function. Use the graph to approximate the indicated extrema. (a) Maximize z = xy; Constraint: 2x + y = 4 .C =2 c 4 = 6 (b) Minimize z =x2 + y2; Constraint: x + y - 4 = 0 Need Help? Talk to a Tutor The graphs show the constraint and several level curves of the objective function. Use the graph to approximate the indicated extrema. (a)...
Consider the following linear program: Max 2X + 3Y s.t. 5X +5Y ≤ 400 -1X+ 1Y ≥ 10 1X + 3Y ≥ 90 X, Y ≥ 0 a. Use the graphical solution procedure to find the optimal solution. b. Conduct a sensitivity analysis to determine the range of optimality for the objective function coefficients X & Y. c. What are the binding constraints? d. If the right-hand-side of the binding constraints are marginally increased, what will be the Dual Value?
Given the following linear optimization problem Maximize 10x + 20y Subject to x+y ≤ 50 2x + 3y ≤ 120 X ≥ 10 X,y≥0 (a) Graph the constraints and determine the feasible region. (b) Find the coordinates of each corner point of the feasible region (c) Determine the optimal solution and optimal objective function value.
Consider the following integer program Max 2x+3y s.t 6x+7y23 x-y<12 xy0 x,y: integer Let V1 denote the optimal objective value of the above optimization problem. Let V2 denote the optimal objective value of the optimization problem obtained by dropping "x,y: integer" constraint. Similarly, let V3 denote the optimal objective value of the optimization problem obtained by dropping "x-y<-12" constraint which one of the following statements is correct? a. V2 V1 and V3<-V1 b. V1 V2 and V1<-V3 c. V2V1 but...
Minimize the objective function 1/2x+3/4y subject to the constraints (In graph form please) 2x+2y>=8 3x+5y>=16 x>=0, y>=0
Quiz: Quiz 2 This Question: 1 pt Minimize the objective function 3x+3y subject to the constraints 2xty 2 13 x+2y 2 14 x20, y20 The minimum value of the function is Simplify your answer.) The value of x is Simplify your answer.) The value of y is Simplify your answer.) Quiz: Quiz 2 This Question: 1 pt Minimize the objective function 3x+3y subject to the constraints 2xty 2 13 x+2y 2 14 x20, y20 The minimum value of the function...
3. Consider the linear programming problem with objective function Q = 4x – 3y and constraints: 9x + 4y > 180, 3x + 8y > 120, 0 < x < 35, y > 0. Graph all constraints and show the feasible region and all corner points. Can the objective function be maximized? If so, find the maximum value of Q.
Figure 5 Constraint 2 Iso-profit line (objective function) 3 2 А B 4 x2 с 1 6 Constraint 1 5 D E x1 24. For a problem with the same constraints as in figure 5 but a different objective function, it was found that the optimal solution was at point A. At point A, which constraint or constraints are binding? Select all that apply. a. X1 >=0 b. x2 >=0 C. Constraint 1 d. Constraint 2