TRUE OR FALSE An optimal solution to a linear programming problem always occurs at the intersection of two constraints.
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TRUE OR FALSE
An optimal solution to a linear programming problem always occurs at the intersection of two constraints.
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- A feasible solution is one that satisfies all the constraints of a linear programming problem simultaneously. Group startsTrue or False True, False,If you add a constraint to an optimization model, andthe previously optimal solution satisfies the new constraint, will this solution still be optimal with the newconstraint added? Why or why not?The optimal solution to any linear programming problem is the same as the optimal solution to the standard form of the problem. TRUE OR FALSE
- In the graphical analysis of a linear programming model,what occurs when the slope of the objective function is thesame as the slope of one of the constraint equations?TRUE OR FALSE Because the constraints to a linear programming problem are always linear, we can graph them by locating only two different points on the line.suppose a linear programming (maximation) problem has been solved and that the optimal value of the objective function is $300. Suppose an additional constraint is added to this problem. Explain how this might affect the optimal value of the objective function.
- What happens when the slope of the objective function is the same as the slope of one of the constraint equations in a graphical analysis of a linear programming model?The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2. Max 3x1 + x2 s.t. 4x1 + x2 ≤ 400 4x1 + 3x2 ≤ 600 x1 + 2x2 ≤ 300 x1, x2 ≥ 0 Over what range can the coefficient of x1 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) Compute the dual value for the third constraint.A linear programming problem is given as follows:min Z = −4x1 + x2Subject to 8x1 + 2x2 ≥ 164x1 + 2x2 ≤ 12x1 ≤ 6x2 ≤ 4x1, x2 ≥ 0 IV) What is the solution of the optimization problem? (x1=?,x2=?,z=?) Show your work V) Which change will make the problem have multiple optimal solutions? If there is more than one answer, choose all.a) Increase of the coefficient of x1 on the objective function to 4b) Increase of the coefficient of x1 on the objective function to 2c) Decrease of the coefficient of x1 on the objective function to -8d) Increase of the coefficient of x2 on the objective function to -8e) None VI) If new constraints, x1≤4 and x2≤6, are added to the given problem, what effect will be? (choose all the effects)a) The feasible solution area will be smaller.b) The feasible solution area will be larger.c) The given problem becomes infeasible.d) The optimal point will be changed.e) The objective value will be decreased.f) There will be no effect.
- The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2. Max 6x1 + 3x2 s.t. 4x1 + x2 ≤ 400 4x1 + 3x2 ≤ 600 x1 + 2x2 ≤ 300 x1, x2 ≥ 0 (a) Over what range can the coefficient of x1 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) ------ to -------- (b) Over what range can the coefficient of x2 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) ----- to -------- (c) Compute the dual value for the first constraint, second constraint & third constraintA linear programming problem is given as follows: Minimize Z = -4x1 + x2 Subject to 8x1 + 2x2 =>16 4x1 + 2x2 =<12 x1 =<5 x2=<2 x1, x2 =>0 Identify the feasible solution area graphically.