1. The following linear programming problem is given: 1(x)-9z1 + 5x2 + 5x3 → maximize under constraints: 22 S 5 9r1 +42 +4z354 1 1-229 1 20,2 20 (a) Write it is the standard form. (b) Find a vert...
1. Solving the linear programming problem Maximize z 3r1 2r2 3, subject to the constraints using the simplex algorithm gave the final tableau T4 T5 #210 1-1/4 3/8-1/812 0 0 23/4 3/8 7/8 10 (a) (3 points) Add the constraint -221 to the final tableau and use the dual simplex algorithm to find a new optimal solution. (b) (3 points) After adding the constraint of Part (a), what happens to the optimal solution if we add the fourth constraint 2+...
Problem #5 -- Consider the following linear programming problem: Maximize Z = 2x1 + 4x2 + 3x3 subject to: X1 + 3x2 + 2x3 S 30 best to X1 + x2 + x3 S 24 3x1 + 5x2 + 3x3 5 60 and X120, X220, X3 2 0. You are given the information that x > 0, X2 = 0, and x3 >O in the optimal solution. Using the given information and the theory of the simplex method, analyze the...
Problem 1: Consider the following linear optimization problem: max +22 +rs subject to X1 + X2 + X3 = 10 2x1 - 22 24 i 20, 1,2,3. (a) Bring the problem to a standard form. (b) Show that the point (2,8,0)Ts optimal by the optimality condition of the linear program- ming. Is it an extreme point? Provide arguments for your answers. (c) Determine at least one other point different than (2,8,0)T, which is an extreme point of the constraint set...
Consider the following minimum problem: Minimize: C = 22 Subject to the constraints: 1 +5:03 > 10 -621 +5x2 > 3 X>0 22 > 0 Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem). P= (Select) Y1+ (Select) Y2 [ Select) Y1+ (Select) Y2 50 (Select) Yi+ 10 Y2 <1 yı >0; 92 > 0
1. -18 points TanFin11 4.1.002. Consider the following linear programming problem. Maximize P 4x + 7y subject to the constraints -2x -3y 2-18 (a) Write the linear programming problem as a standard maximization problem. MaximizeP subject to s 12 s 18 (b) Write the initial simplex tableau Constant 12 18 0 Submit Answer Save Progress
16.10 Consider the linear programming problem minimze -T subject to 1-2-1 T1,2 20 a. Write down the basic feasible solution for z as a basic variable. b. Compute the canonical augmented matrix corresponding to the basis in part a c. If we apply the simplex algorithm to this problem, under what circum stance does it terminate? (In other words, which stopping criterion in the simplex algorithm is satisfied?) d. Show that in this problem, the objective function can take arbitrarily...
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...
Linear Programming Problem A manufacturer of three models of tote bag must determine the production plan for the next quarter. The specifics for each model are shown in the following table. Model Revenue ($ per item) Cutting (hours per item) Sewing (hours per item) Packing (hours per item) A $8.75 .10 .05 .20 B $10.50 .15 .12 .20 C $11.50 .20 .18 .20 Time available in the three production departments are: Cutting 450 hours, Sewing 550 hours, Packing 450 hours....
Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) 2) 3) Every basic solution in the assignment problem is necessarily degenerate. The assignment problem cannot be solved using the transportation technique. If the gradient vector of a function at a given point is zero, the point can only be a maximum or minimum. If a single-variable function has two local minima, it must have at least one local 4) maximum 5) The Golden...
#5 urgent need now Linear Programming: 4. Kings Department Store has 625 nubies, 800 diamonds, and 700 emeraids from which they will make bracelets and necklaces that they have advertised in their Christmas brochure. Each of the rubies is approximately the same size and shape as the diamonds and the emeralds Kings will net a profit of S250 on each bracelet, which is made with 2 nubies, 3 diamonds, and 4 emeralds, and $500 on each necklace, which includes 5...