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Figure 5 Constraint 2 Iso-profit line (objective function) 3 2 А B 4 x2 с 1...
Given: Objective function: maximize Z = 6x1+ 7x2 Constraints: x1 + 3 x2 30 4...
Given: Objective function: maximize Z = 6x1+ 7x2 Constraints: x1 + 3 x2 30 4 x1 + x2 32 x1 ≥ 0, x2 ≥ 0 a) Use graphical method to determine the optimal solution and the optimal value for Z.Use EXCEL to determine the optimal solution and the optimal value for Z.
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2...
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2 〈 24 1xl t 2x2< 16 And xl, x2> 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of xl, x2, and Z. b) Assume that the objective function coefficient for xl changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective...
Vertex x1 x2 1 2 3 x1 x2 optimal vertex optimal objective function value
Vertex
x1
x2
1
2
3
x1
x2
optimal vertex
optimal objective function value
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 Constraint 2:x+2ys8 Constraint 3 x-3y 2-2 2x-v21 2r-y-1 4 4 6 b. (3 points) The objective function is Minimize 2x-3y. Mark the optimal solution(s) n 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)
If the per unit profit associated with producing the standard glove were to increase by $3...
If the per unit profit associated with producing the standard glove were to increase by $3 a pair, what would the impact be on the total profit? Obje ctive Cell (Max) Original Value Final Value Cell Name $B54 Obje ctive Function (Maxim ize Profit) 218 Variable Cells Integer 18 Contin 16 Contin Original Value Final Value Cell Name $B$1 X1(#of standard gloves) $852 X2(#of deluxe gloves) Constraints Cell Cell Value Formula Status Slack Name $B$8 1) Constraint#1 (le ather cutting...
For Questions 1, consider the following classifications: Feasible Region I- Finite Line Segment II -Non-existent III...
For Questions 1, consider the following classifications: Feasible Region I- Finite Line Segment II -Non-existent III - Polygon IV-Single Point V - Unbounded Optimal Solution A -Alternate Optima B-No feasible solution C- Unbounded D-Unique 1. Suppose an LP with 5 regular constraints (other than the non-negativity constraints) has "lr as its feasible region. If a new constraint is added, which of the following CANNOT be the type of the new optimal solution? a, A b. В с. С d. De,...
Consider the following constraints and the c g graph below: Constraint L:4x-y21 Constraint 2: x+ys4 Constraint...
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...
Your problem will have exactly two variables (an X1 and an X2) and will incorporate a maximization (either profit or revenue) objective. You will include at least four constraints (not including the X...
Your problem will have exactly two variables (an X1 and an X2) and will incorporate a maximization (either profit or revenue) objective. You will include at least four constraints (not including the X1 ≥ 0 and X2 ≥ 0 [i.e., the “Non-negativity” or “Duh!”] constraints). At least one of these four must be a “≤” constraint, and at least one other must be a “≥” constraint; do not include any “= only” constraints. You must have a unique Optimal Solution...
Figure 1 provides the Excel Sensitivity output for the following LP model. 10x1 + 8x2 Max...
Figure 1 provides the Excel Sensitivity output for the following LP model. 10x1 + 8x2 Max Z= subject to: 31 +2x2 < 24 2x1 + 4x2 = 12 -2x1 + 2 x2 56 X1, X2 > 0 Variable Cells Cell Name $B$13 Solution x1 $C$13 Solution x2 Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 6 0 10 1E+30 0 -12 8 12 1E+30 6 Constraints Cell $D$6 $D$7 $D$8 Name C1 Totals C2 Totals C3 Totals Final...
Find the solution of the objective function for problems (a) - (b) below. For each problem,...
Find the solution of the objective function for problems (a) -
(b) below. For each problem, confirm that the optimum satisfies the
Kuhn-Tucker conditions. At each solution, describe whether the
constraint(s) is binding.
Mathematics for Economists Ken Danger Problem Set 13 1) Find the solution of the objective function for problems (a) - (b) below. For each problem, confirm that the optimum satisfies the Kuhn-Tucker conditions. At each solution, describe whether the constraint(s) is binding. a) Minimize the cost function...
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2 〈 24 1xl t 2x2< 16 And xl, x2> 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of xl, x2, and Z. b) Assume that the objective function coefficient for xl changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective...
Vertex
x1
x2
1
2
3
x1
x2
optimal vertex
optimal objective function value
Consider the following constraints and the corresponding graph below: Constraint 1 Constraint 2:x+2ys8 Constraint 3 x-3y 2-2 2x-v21 2r-y-1 4 4 6 b. (3 points) The objective function is Minimize 2x-3y. Mark the optimal solution(s) n 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)
If the per unit profit associated with producing the standard glove were to increase by $3 a pair, what would the impact be on the total profit? Obje ctive Cell (Max) Original Value Final Value Cell Name $B54 Obje ctive Function (Maxim ize Profit) 218 Variable Cells Integer 18 Contin 16 Contin Original Value Final Value Cell Name $B$1 X1(#of standard gloves) $852 X2(#of deluxe gloves) Constraints Cell Cell Value Formula Status Slack Name $B$8 1) Constraint#1 (le ather cutting...
For Questions 1, consider the following classifications: Feasible Region I- Finite Line Segment II -Non-existent III - Polygon IV-Single Point V - Unbounded Optimal Solution A -Alternate Optima B-No feasible solution C- Unbounded D-Unique 1. Suppose an LP with 5 regular constraints (other than the non-negativity constraints) has "lr as its feasible region. If a new constraint is added, which of the following CANNOT be the type of the new optimal solution? a, A b. В с. С d. De,...
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...
Figure 1 provides the Excel Sensitivity output for the following LP model. 10x1 + 8x2 Max Z= subject to: 31 +2x2 < 24 2x1 + 4x2 = 12 -2x1 + 2 x2 56 X1, X2 > 0 Variable Cells Cell Name $B$13 Solution x1 $C$13 Solution x2 Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 6 0 10 1E+30 0 -12 8 12 1E+30 6 Constraints Cell $D$6 $D$7 $D$8 Name C1 Totals C2 Totals C3 Totals Final...
Find the solution of the objective function for problems (a) -
(b) below. For each problem, confirm that the optimum satisfies the
Kuhn-Tucker conditions. At each solution, describe whether the
constraint(s) is binding.
Mathematics for Economists Ken Danger Problem Set 13 1) Find the solution of the objective function for problems (a) - (b) below. For each problem, confirm that the optimum satisfies the Kuhn-Tucker conditions. At each solution, describe whether the constraint(s) is binding. a) Minimize the cost function...
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