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1) Consider the following model: Minimize Z - 40x, +50x, subject to: 2x, + 3x, 2...
Solve the linear programming problem. Minimize and maximize z=50x+10y Subject to 2x+y ≥ 32 x+y ≥...
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
Finite Math MIXED CONSTRANTS 3. Minimize z = 18x3 + 24x2, subject to 3x, +4x, 2...
Finite Math
MIXED CONSTRANTS
3. Minimize z = 18x3 + 24x2, subject to 3x, +4x, 2 48 x + 2x, s 22 3x + 2x, S 42 X, X, 20 4. Minimize z = 8x1 + 10x2 + 25x3, subject to x + x3 30 2x, + 4x2 + 5x, 270 2x2 + x3 2 27 X, X2,43 20
Must show all work 4. (10 pts) Consider the following problem. Minimize Z=3x2+2 xZ+X3, Maximize subject...
Must show all work
4. (10 pts) Consider the following problem. Minimize Z=3x2+2 xZ+X3, Maximize subject to subject to (constraint 1) x2+x2=7 (constraint 1) (constraint 2) 3x2+x2+x,210 (constraint 2) (constraint 3) X2-4 x32-8 (constraint 3) (constraint 4) x 21 and (all decision variables nonnegativel and x >0 (no nonnegativity constraint on x.i. (a) (5 pts) Convert this problem to a maximization problem with only three functional constraints, all constraints' RHS are non negative, and all decision variables need to satisfy...
PROBLEMS 7.3 1. Minimize Z= 6x + 14y subject to 14x + 7y > 43 3x...
PROBLEMS 7.3 1. Minimize Z= 6x + 14y subject to 14x + 7y > 43 3x + 7y > 21 --x+y> -5 x,y > 0 2. Maximize Z= 2x + 2y subject to 2x - y > -4 x - 2y < 4 x+y = 6 Xy0
8. Minimize z - 8x1 + 6x2 + 11x3 subject to 5x1 x2 + 3x3 s 4 5x1 + x2 + 3x3 2 2 2x, + 4x2 + 7x3 s...
8. Minimize z - 8x1 + 6x2 + 11x3 subject to 5x1 x2 + 3x3 s 4 5x1 + x2 + 3x3 2 2 2x, + 4x2 + 7x3 s.5 2x1 + 4x2 + 7x3 2 3 X1 + X2 + X3 = 1 (a) State the dual problem. (b) Solve both the primal and the dual problem with any method that works. (c) Check that your optimal solutions are correct by verifying they are feasible and the primal and...
Minimize the objective function 1/2x+3/4y subject to the constraints (In graph form please) 2x+2y>=8 3x+5y>=16 x>=0,...
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
3. For the following linear programming (primal) problem Minimize Z -3x1 x2 - 2x3, subject to xx2...
question e
3. For the following linear programming (primal) problem Minimize Z -3x1 x2 - 2x3, subject to xx2 2x3 s 20 2xl x2 - x3 < 10 and xl20, x220, x32 0. (a) Find a standard form of the given problem and solve the problem using simplex (b) Find marginal costs corresponding each constraint of the primal (c) If we change the right hand side of the first constraint (10) to 10+A, then draw a graph representing the optimal...
a) Solve the following problem using graphical method (using the following graph): Minimize f(x,y) - 2x-y...
a) Solve the following problem using graphical method (using the following graph): Minimize f(x,y) - 2x-y subject to the constraints x2+y's 20 y<x (1) (2) (In the space provided below the graph, please write down your solution clearly) we wish to solve the above problem using Exterior Penalty Function approach. Define b) Suppose augmented cost function and explain how to use it to find a solution to the above problem.
a) Solve the following problem using graphical method (using the...
Maximize and minimize p = 2x − y subject to x + y ≥ 1 x...
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.) Maximize and minimize p = 2x - y subject...
Operations Research Problem 2. Consider the following program: Minimize 2 22 subject to+ x2 s2 2x1...
Operations Research
Problem 2. Consider the following program: Minimize 2 22 subject to+ x2 s2 2x1 + 3x2 21 xi r2 21 Please solve the problem graphically and perform sensitivity analysis (along the lines of Supple- mentary text): (a) determine the amount of slack (or unused surplus) in the constraints at the optimal solu tion; )etie shadow prices/reduced s ociated with the constraints (c) for the binding constraints, determine the ranges for the right-hand side coefficients such that the constraints...
Finite Math
MIXED CONSTRANTS
3. Minimize z = 18x3 + 24x2, subject to 3x, +4x, 2 48 x + 2x, s 22 3x + 2x, S 42 X, X, 20 4. Minimize z = 8x1 + 10x2 + 25x3, subject to x + x3 30 2x, + 4x2 + 5x, 270 2x2 + x3 2 27 X, X2,43 20
Must show all work
4. (10 pts) Consider the following problem. Minimize Z=3x2+2 xZ+X3, Maximize subject to subject to (constraint 1) x2+x2=7 (constraint 1) (constraint 2) 3x2+x2+x,210 (constraint 2) (constraint 3) X2-4 x32-8 (constraint 3) (constraint 4) x 21 and (all decision variables nonnegativel and x >0 (no nonnegativity constraint on x.i. (a) (5 pts) Convert this problem to a maximization problem with only three functional constraints, all constraints' RHS are non negative, and all decision variables need to satisfy...
PROBLEMS 7.3 1. Minimize Z= 6x + 14y subject to 14x + 7y > 43 3x + 7y > 21 --x+y> -5 x,y > 0 2. Maximize Z= 2x + 2y subject to 2x - y > -4 x - 2y < 4 x+y = 6 Xy0
8. Minimize z - 8x1 + 6x2 + 11x3 subject to 5x1 x2 + 3x3 s 4 5x1 + x2 + 3x3 2 2 2x, + 4x2 + 7x3 s.5 2x1 + 4x2 + 7x3 2 3 X1 + X2 + X3 = 1 (a) State the dual problem. (b) Solve both the primal and the dual problem with any method that works. (c) Check that your optimal solutions are correct by verifying they are feasible and the primal and...
question e
3. For the following linear programming (primal) problem Minimize Z -3x1 x2 - 2x3, subject to xx2 2x3 s 20 2xl x2 - x3 < 10 and xl20, x220, x32 0. (a) Find a standard form of the given problem and solve the problem using simplex (b) Find marginal costs corresponding each constraint of the primal (c) If we change the right hand side of the first constraint (10) to 10+A, then draw a graph representing the optimal...
a) Solve the following problem using graphical method (using the following graph): Minimize f(x,y) - 2x-y subject to the constraints x2+y's 20 y<x (1) (2) (In the space provided below the graph, please write down your solution clearly) we wish to solve the above problem using Exterior Penalty Function approach. Define b) Suppose augmented cost function and explain how to use it to find a solution to the above problem.
a) Solve the following problem using graphical method (using the...
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.) Maximize and minimize p = 2x - y subject...
Operations Research
Problem 2. Consider the following program: Minimize 2 22 subject to+ x2 s2 2x1 + 3x2 21 xi r2 21 Please solve the problem graphically and perform sensitivity analysis (along the lines of Supple- mentary text): (a) determine the amount of slack (or unused surplus) in the constraints at the optimal solu tion; )etie shadow prices/reduced s ociated with the constraints (c) for the binding constraints, determine the ranges for the right-hand side coefficients such that the constraints...
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