New Semester Started Get 50% OFF Study Help! --h --m --s Claim Now

Question Answers

Textbooks

Find textbooks, questions and answers

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
business
operations research an introduction

Optimization In Operations Research 2nd Edition Ronald Rardin - Solutions

Determine whether acyclic shortest path Algorithm 9D could be applied to compute shortest paths from node 1 to all other nodes in each digraph of Exercise 9-17. If so, explain whether it would be more efficient than the Bellman–Ford, Floyd–Warshall, and Dijkstra alternatives, and why.
Do Exercise 9-15 on the graph of Exercise 9-2.
Return to the graph of Exercise 9-1, and suppose that we seek shortest paths from node 1 to all other nodes.(a) Explain why Dijkstra Algorithm 9C can be employed to compute the required shortest paths.(b) Apply Algorithm 9C to compute the length of shortest paths from node 1 to all other nodes.(c)
Use Floyd–Warshall Algorithm 9B to identify a negative dicycle in each of the following graphs.(a) The digraph of Exercise 9-7(b) The digraph of Exercise 9-8
Do Exercise 9-12 on the graph of Exercise 9-6.
Return to the graph of Exercise 9-5, and suppose that we seek shortest paths from all nodes to all other nodes.(a) Explain why Floyd–Warshall Algorithm 9B can be employed to compute the required shortest paths.(b) Apply Algorithm 9B to compute the length of shortest paths from all nodes to all
Use Bellman–Ford Algorithm 9A to identify a negative dicycle in each of the following graphs.(a) The digraph of Exercise 9-7(b) The digraph of Exercise 9-8
Do Exercise 9-9 on the graph of Exercise 9-2.
Return to the graph of Exercise 9-1, and suppose that we seek shortest paths from node 1 to all other nodes.(a) Explain why Bellman–Ford Algorithm 9A can be employed to compute the required shortest paths.(b) Apply Algorithm 9A to compute the lengths of shortest paths from node 1 to all other
Do Exercise 9-3 for the problem of Exercise 9-2, verifying the optimal 1 to 3 path in part (b).
Return to the problem of Exercise 9-1.(a) Find (by inspection) shortest paths from node 1 to all other nodes.(b) Verify that every subpath of the optimal 1 to 2 path in part (a) is itself optimal.(c) Detail your optimal solutions of part (a)in functional notation n[k] and xi,j[k].(d) Write
Consider the linear constraints-w1 + w2 … 1 w2 … 3 w1, w2 Ú 0(a) Sketch the feasible space in a 2-dimensional plot.(b) Determine geometrically whether each of the following solutions are infeasible, boundary, extreme, and/or interior:w112 = (2, 3),w122 = 10, 32, w132 = 12, 12, w142 = (3, 3),
Do Exercise 5-1 for the LP 3w1 + 5w2 … 15 5w1 + 3w2 … 15 w1, w2 Ú 0 and points w112 = 10, 02, w122 = 11, 12, w132 =12, 02, w142 = 13, 32 and w152 = 15, 02.
Place each of the following LPs in standard form and identify the corresponding A,b, and c of definition 5.4 .(a) min 4x1 + 2x2 - 33x3 s.t. x1 - 4x3 + x3 … 12 9x1 + 6x3 = 15-5x1 + 9x2 Ú 3 x1, x2, x3 Ú 0(b) max 45x1 + 15x3 s.t. 4x1 - 2x2 + 9x3 Ú 22-2x1 + 5x2 - x3 = 1 x1 - x2 … 5 x1, x2, x3 Ú
Consider the linear constraints-y1 + y2 … 2 5y1 … 10 y1, y2 Ú 0(a) Sketch the feasible set in a 2-dimensional plot.(b) Add slacks y3 and y4 to place constraints in LP standard form.(c) Determine whether columns of standard form corresponding to each of the following sets of variables form a
Do Exercise 5-4 for the LP y1 + 2y2 … 6 y2 … 2 y1, y2 Ú 0 and possible basic sets 5y1, y26,5y2, y36,5y16, 5y2, y46,5y2, y3, y46,5y1, y36.
Write all conditions that a feasible directionw must satisfy, at the solution w indicated, to each of the following standard-form systems of LP constraints.(a) 5w1 + 1w2 - 1w3 = 9 at w = 12, 0, 12 3w1 - 4w2 + 8w3 = 14 w1, w2, w3 Ú 0(b) 4w1 - 2w2 + 5w3 = 34 at w = 11, 0, 62 4w1 + 2w2 - 3w3 = -14
Following is a maximizing, standard-form linear program and a classification of variables as basic and nonbasic.x1 x2 x3 x4 max c 10 1 0 0 b-1 1 4 21 13 2 6 0 -2 2 B N B B(a) Compute the current basic solution.(b) Compute all simplex directions available at the current basis.(c) Verify that all
Do Exercise 5-7 for minimizing the standard form LP x1 x2 x3 x4 min c 8 -5 0 1 b 13 2 3 1 7-4 1 0 -1 -1 N N B B
Consider the linear program max 3 z1 + z2 s.t. -2z1 + z2 … 2 z1 + z2 … 6 z1 … 4 z1, z2 Ú 0(a) Solve the problem graphically.(b) Add slacks z3, z4, and z5 to place the model in standard form.(c) Apply rudimentary simplex Algorithm 5A to compute an optimal solution to your standard form
Do Exercise 5-9 for the LP max 2 z1 + 5z2 s.t. 3z1 + 2z2 … 18 z1 … 5 z2 … 3 z1, z2 Ú 0
Consider the linear program max 10y1 + y2 s.t. 3y1 + 2y2 Ú 6 2y1 + 4y2 … 8 y1, y2 Ú 0(a) Solve the problem graphically. Be sure to identify all constraints, show contours of the objective, outline the feasible space, and justify that an optimal solution is y1 * = 4, y2 * = 0.(b) Place the above
Consider the standard-form linear program min x2 + x4 + x5 s.t. -2x1 + x2 + 2x4 = 7 x4 + x5 = 5 x2 + x3 - x4 = 3 x1,c, x5 Ú 0(a) Compute the basic solution corresponding to x1, x3, x4 basic, and explain why it provides an appropriate place for the rudimentary simplex Algorithm 5A to begin its
Do Exercise 5-12 on standard-form linear program max 5x1 - 10x2 s.t. 1x1 - 1x2 + 2x3 + 4x5 = 2 1x1 + 1x2 + 2x4 + x5 = 8 x1,c, x5 Ú 0 starting with x3 and x4 basic.
Do Exercise 5-12 on standard-form linear program min 2 x1 + 4x2 + 6x3 + 10x4 + 7x5 s.t. x1 + x4 = 6 x2 + x3 - x4 + 2x5 = 9 x1,c, x5 Ú 0 starting with x1 and x2 basic.
The following plot shows several feasible points in a linear program and contours of its objective function.Determine whether each of the following sequences of solutions could have been one followed by the simplex algorithm applied to the corresponding LP standard form.(a) P1,P8,P7,P6 (b)
Construct the simplex dictionary form 5.28 corresponding to each of the following.(a) The model and basis shown in Exercise 5-7(b) The model and basis shown in Exercise 5-8
Rudimentary simplex Algorithm 5A is being applied to optimize a linear program with objective function min 3w1 + 11w2 - 8w3 Determine whether each of the following simplex directions for w4 leads to a conclusion that the given LP in unbounded.(a) w = 11, 0, -4, 12(b) w = 11, 3, 10, 12(c) w = 11,
Consider the linear program max 4y1 + 5y2 s.t. -y1 + y2 … 4 y1 - y2 … 10 y1, y2 Ú 0(a) Show graphically that the model is un bounded.(b) Add slacks y3 and y4 to place the model in standard form.(c) Starting with all slacks basic, apply rudimentary simplex Algorithm 5A to establish that the
Do Exercise 5-18 for the LP min -10y1 + y2 s.t. -5y1 + 3y2 … 15 3y1 - 5y2 … 8 y1, y2 Ú 0
Setup each of the following to begin Phase I of two-phase simplex Algorithm 5B. Also indicate the basic variables of the initial Phase I solution.(a) max 2 w1 + w2 + 9w3 s.t. w1 + w2 … 18-2w1 + w3 = -2 3w2 + 5w3 Ú 15 w1, w2, w3 Ú 0(b) max 5 w1 + 18w2 s.t. 2w1 + 4w2 = 128 7w1 + w2 Ú 11 6w1 +
Setup each of the models in Exercise 5-20 to begin a big-M solution using rudimentary simplex Algorithm 5A. Also indicate the basic variables of the initial solution.
Consider the linear program max 9 y1 + y2 s.t. -2y1 + y2 Ú 2 y2 … 1 y1, y2 Ú 0(a) Show graphically that the model is infeasible.(b) Add slacks and artificials y3,c, y5 to setup the model for Phase I of Algorithm 5B.(c) Apply rudimentary simplex Algorithm 5A to this Phase I problem to establish
Do Exercise 5-22 for the linear program min 2 y1 + 8y2 s.t. y1 + y2 … 5 y2 Ú 6 y1, y2 Ú 0
Assuming that step size l 7 0 at every step, compute a finite bound on the number of iterations of Algorithm 5A for each of the following standard-form linear programs.(a) The model in Exercise 5-7(b) The model in Exercise 5-8(c) A model with 1150 main constraints and 2340 variables(d) A model with
Rudimentary simplex Algorithm 5A is being applied to a standard-form linear program with variables x1,c, x5. Determine whether each of the following basic solutions is degenerate for the given basic variable set.(a) B = 5x1, x2, x36, x = 11, 0, 5, 0, 02 (b) B = 5x3, x4, x56, x = 10, 0, 1, 0, 92 (c)
Return to Exercise 5-4 and consider adding additional constraint y2 … 4 to the original LP.(a) Repeat parts (a)-(c) of Exercise 5-4 with the extra constraint, and additional slack y5 included in all potential basis sets of part (c).(b) Demonstrate that in your revised standard form LP has 3
Do Exercise 5-26 on the LP of Exercise 5-5 with additional constraint y1 … 6 and focusing degeneracy parts on extreme point 1y1, y22 =16, 02.
Consider the linear program max x 1 + x2 s.t. x1 + x2 … 9-2x1 + x2 … 0 x1 - 2x2 … 0 x1, x2 Ú 0(a) Solve the problem graphically.(b) Add slacks x3,c, x5 to place the model in standard form.(c) Apply rudimentary simplex Algorithm 5A to compute an optimal solution to your standard form starting
Do Exercise 5-28 for the LP max x 1 s.t. 6x1 + 3x2 … 18 12x1 - 3x2 … 0 x1, x2 Ú 0
Return to the LP of Exercise 5-7.(a) Compute the basis matrix inverse corresponding to the basic variables indicated.(b) Compute the corresponding pricing vector of 5.45 .(c) Without generating the implied simplex directions, use your pricing vector to determine whether each of them will be
Do Exercise 5-30 for the LP of Exercise 5-8.
Consider applying revised simplex Algorithm 5C to the tabulated standard-form LP min c =x1 x2 x3 x4 x5 5 4 3 2 16 b A = 2 0 1 0 6 8 0 1 1 2 3 12 starting with x1 and x2 basic.(a) Determine the corresponding starting basis matrix and its inverse, along with the associated primal basic solution and
Solve each of the following standard form linear programs by revised simplex Algorithm 5C, showing the basic inverse, the pricing vector, and update matrix E used at each iteration. Start from the basis specified in each original exercise.(a) The LP of Exercise 5-12.(b) The LP of Exercise 5-13.(c)
Suppose lower- and upper-bounded simplex Algorithm 5D is being applied to a problem with objective function max 3x1 - 4x2 + x3 - 4x4 + 10x5 3 main constraints, and bounds 0 … xj … 5 j = 1,c, 5 For each of the following current basic solutions x and corresponding simplex directions x, determine
Consider the linear program min 5z1 + 6z2 s.t. z1 + z2 Ú 3 3z1 + 2z2 Ú 8 0 … z1 … 6 0 … z2 … 5(a) Solve the problem graphically.(b) Add slacks z3 and z4 to place the model in standard form for a lower- and upperbounded simplex.(c) Apply lower- and upper-bounded simplex Algorithm 5D to
Do Exercise 5-35 on the LP max 6 z1 + 8z2 s.t. z1 + 3z2 … 10 z1 + z2 … 5 0 … z1 … 4 0 … z2 … 3 Start with original variable z1 nonbasic lowerbounded and z2 upper-bounded.
Solve each of the following standard form linear programs by lower- and upper-bounded simplex Algorithm 5D, showing the basic inverse, the pricing vector, and update matrix E used at each iteration.(a) The LP of Exercise 5-12 with added upper bounds xj … 3, j = 1,c, 5, starting with x1, x3, x5
As a result of a recent decision to stop production of toy guns that look too real, the Super Slayer Toy Company is planning to focus its production on two futuristic models: beta zappers and freeze phasers. Beta zappers produce $2.50 in profit for the company, and freeze phasers, $1.60.The company
Eli Orchid can manufacture its newest pharmacutical product in any of three processes.One costs $14,000 per batch, requires 3 tons of one major ingredient and 1 ton of the other, and yields 2 tons of output product. The second process costs $30,000 per batch, requires 2 and 7 tons of the
Professor Proof is trying to arrange for the implementation in a computer program of his latest operations research algorithm. He can contract with any mix of three sources for help:unlimited hours from undergraduates at $4 per hour, up to 500 hours of graduate students at $10 per hour, or
The NCAA is making plans for distributing tickets to the upcoming regional basketball championships. The up to 10,000 available seats will be divided between the media, the competing universities, and the general public. Media people are admitted free, but the NCAA receives$45 per ticket from
For each of the following constraint coefficient changes, determine whether the change would tighten or relax the feasible set, whether any implied change in the optimal value would be an increase or a decrease, and whether the rate of any such optimal value effect would become more or less steep
Determine whether adding each of the following constraints to a mathematical program would tighten or relax the feasible set and whether any implied change in the optimal value would be an increase or a decrease. Assume that the constraint is not the only one.(a) Maximize problem, 2w1 + 4w2 Ú
For each of the following objective coefficient changes, determine whether any implied change in the optimal value would be an increase or a decrease and whether the rate of any such optimal value effect would become more or less steep if it varied with the magnitude of coefficient change. Assume
Return to Super Slayer Exercise 6-1.(a) Assign dual variables to each main constraint of the formulation in part (a), and define their meanings and units of measurement.(b) Show and justify the appropriate variable-type restrictions on all dual variables.(c) Formulate and interpret the main dual
Do Exercise 6-8 for the problem of Exercise 6-2 using Table 6.7.
Do Exercise 6-8 for the problem of Exercise 6-3 using Table 6.8.
Do Exercise 6-8 for the problem of Exercise 6-4 using Table 6.9.
State the dual of each of the following LPs.(a) min 17x1 + 29x2 + x4 s.t. 2x1 + 3x2 + 2x3 + 3x4 … 40 4x1 + 4x2 + x4 Ú 10 3x3 - x4 = 0 x1,c, x4 Ú 0(b) min 44x1 - 3x2 + 15x3 + 56x4 s.t. x1 + x2 + x3 + x4 = 20 x1 - x2 Ú 0 9x1 - 3x2 + x3 - x4 … 25 x1,c, x4 Ú 0(c) max 30x1 - 2x3 + 10x4 s.t. 2x1
State (primal and dual) complementary slackness conditions for each LP in Exercise 6-12.
Each of the following LP has a finite optimal solution. State the corresponding dual, solve both primal and dual graphically, and verify that optimal objective function values are equal.(a) max 14x1 + 7x2 s.t. 2x1 + 5x2 … 14 5x1 + 2x2 … 14 x1, x2 Ú 0(b) min 4x1 + 10x2 s.t. 2x1 + x2 Ú 6 x1 Ú
Compute the dual solution corresponding to each of the following basic sets in the standard-form LP max 6x1 + 1x2 + 21x3 - 54x4 - 8x5 s.t. 2x1 + 5x3 + 7x5 = 70+ 3x2 + 3x3 - 9x4 + 1x5 = 1 x1,c, x5 Ú 0(a) 5x1, x26(b) 5x1, x46(c) 5x2, x36(d) 5x3, x56
Each of the following is a linear program with no optimal solution. State the corresponding dual, solve both primal and dual graphically, and verify that whenever primal or dual is unbounded, the other is infeasible.(a) max 4x1 + x2 s.t. 2x1 + x2 Ú 4 3x2 … 12 x1, x2 Ú 0(b) max 4x1 + 8x2 s.t.
For each of the following LPs and solution vectors, demonstrate that the given solution is feasible, and compute the bound it provides on the optimal objective function value of the corresponding dual.(a) min 30x1 + 2x2 and x = 12, 52 s.t. 4x1 + x2 … 15 5x1 - x2 Ú 2 15x1 - 4x2 = 10 x1, x2 Ú
For each of the following, verify that the given formulation is the dual of the referenced primal in Exercise 6-17, demonstrate that the given solution is dual feasible, and compute the bound it provides on the corresponding primal optimal solution value.(a) For 6-17(a) and solution v = 10, 0, 22
Demonstrate for each linear program in Exercise 6-17 that the dual of its dual is the primal.
Razorback Tailgate (RT) makes tents for football game parking lot cookouts at its two different facilities, with two processes that may be employed in each facility. All facilities and processes produce the same ultimate product, and Razorback wants to build 22 in the next 80 business hours. Unit
As spring approaches, the campus grounds staff is preparing to buy 500 truckloads of new soil to add around buildings and in gulleys where winter has worn away the surface. Three sources are available at $220, $270, and $290 per truckload, respectively, but the soils vary in nitrogen and clay
Return to Exercise 6-1. Answer each of the following as well as possible from the results in Table 6.6.(a) Is the optimal solution sensitive to the exact value of the trimming hours available?At what number of hours capacity would it become relevant?(b) How much should Super Slayer be willing to
Return to Eli Orchid Exercise 6-2. Answer each of the following as well as possible from the results in Table 6.7.(a) What is the marginal cost of production(per ton of output)?(b) How much would it cost to produce 70 tons of the new pharmaceutical product?To produce 100 tons?(c) How much should
Return to Exercise 6-3. Answer each of the following as well as possible from the results in Table 6.8.(a) What is the marginal cost per professional-equivalent hour of programming associated with the optimal solution in Table 6.8?(b) How much would cost increase if 1050 professional-equivalent
Return to NCAA ticket Exercise 6-4.Answer each of the following as well as possible from the results in Table 6.9.(a) What is the marginal cost to the NCAA of each seat guaranteed the media?(b) Suppose that there is an alternative arrangement of the dome where the games will be played that can
Paper can be made from new wood pulp, from recycled office paper, or from recycled newsprint. New pulp costs $100 per ton, recycled office paper, $50 per ton, and recycled newsprint,$20 per ton. One available process uses 3 tons of pulp to make 1 ton of paper; a second uses 1 ton of pulp and 4 tons
Silva and Sons Ltd. (SSL)2 is the largest coconut processor in Sri Lanka. SSL buys coconuts at 300 rupees per thousand to produce two grades (fancy and granule) of desiccated (dehydrated)coconut for candy manufacture, coconut shell flour used as a plastics filler, and charcoal.Nuts are first sorted
Tube Steel Incorporated (TSI) is optimizing production at its 4 hot mills. TSI makes 8 types of tubular products which are either solid or hollow and come in 4 diameters. The following two tables show production costs (in dollars) per tube of each product at each mill and the extrusion times (in
Consider the primal linear program max 13z2 - 8z3 s.t. - 3z1 + z3 … 19 4z1 + 2z2 + 7z3 = 10 6z1 + 8z3 Ú 0 z1, z3 Ú 0(a) Formulate the corresponding dual in terms of variables v1, v2, v3.(b) Formulate and justify all Karush-Kuhn-Tucker conditions for primal solution zQ and dual solution vQ to be
Return to the primal LPs of Exercise 6-17 and corresponding duals of Exercise 6-18.(a) State and justify all Karush-Kuhn-Tucker conditions for each pair of models.(b) Compute solution values for primal x in Exercise 6-17 and dual v in Exercise 6-18, and show that their difference is exactly the
Consider the standard-form linear program max 5x1 - 10x2 s.t. 1x1 - 1x2 + 2x3 + 4x5 = 2 1x1 + 1x2 + 2x4 + x5 = 8 x1, x2, x3, x4, x5 Ú 0(a) Taking x1 and x2 as basic, identify all elements of the corresponding partitioned model: B, B-1, N, cB, cN, and b.(b) Then use the partitioned elements of
Return to the standard-form LP of Exercise 6-31, and do parts (a)–(d), this time using basis(x3, x4). Then(e) State all KKT conditions for your primal solution of part (b) and dual solution of part (d) to be optimal in their respective problems.(f) Demonstrate your solutions of parts (b)and (d)
Consider the linear program min 2x1 + 3x2 s.t. -2x1 + 3x2 Ú 6 3x1 + 2x2 Ú 12 x1, x2 Ú 0(a) Establish that subtracting nonnegative surplus variables x3 and x4 leads to the equivalent standard-form:min 2x1 + 3x2 s.t. -2x1 + 3x2 - x3 = 6 3x1 + 2x2 - x4 = 12 x1, x2, x3, x4 Ú 0(b) Solve the original
Consider the linear program min 2x1 + 3x2 + 4x3 s.t. x1 + 2x2 + x3 Ú 3 2x1 - x2 + 3x3 Ú 4 x1, x2, x3 Ú 0(a) Use nonnegative surplus variables x4 and x5 to place the model in standard form.(b) State the dual of your standard form model in part (a) in terms of variables v1 and v2.(c) Choosing x4
Consider the standard form linear program min 3x1 + 4x2 + 6x3 + 7x4 + x5 s.t. 2x1 - x2 + x3 + 6x4 - 5x5 - x6 = 6 x1 + x2 + 2x3 + x4 + 2x5 - x7 = 3 x1,c, x7 Ú 0(a) State the dual of this model using variables v1 and v2.(b) Establish that v1 = v2 = 0 is dual feasible in your formulation of part
Return to the standard-form LP of Exercise 6-33(a).(a) Solve the model by Dual Simplex Algorithm 6A starting from the all surplus basis (x3, x4). At each step, identify the basis matrix B, its inverse B-1, the corresponding primal solution x, the basic cost vector cB, the corresponding dual
Return to the standard-form LP of Exercise 6-34(a).(a) Solve the model by Primal-Dual Simplex Algorithm 6B starting from dual solution v = 10, 02. At each major step, state the restricted primal, the dual solution v, reduced costs on all primal variables, and the direction of change v. Also verify
Consider the following linear program:max 3z1 + z2 s.t. -2z1 + z2 … 2 z1 + z2 … 6 z1 … 4 z1, z2 Ú 0 After converting to standard form, solution of the model via Rudimentary Simplex Algorithm 5A produces the following sequence of steps: (a) State the dual of the standard-form primal depicted
Consider the linear program max 2w1 + 3w2 s.t. 4w1 + 3w2 … 12 w2 … 2 w1, w2 Ú 0(a) Solve the problem graphically.(b) Determine the direction w of most rapid improvement in the objective function at any solution w.(c) Explain why the direction of part (b) is feasible at any interior point
Do Exercise 7-1 for the LP min 9w1 + 1w2 s.t. 3w1 + 6w2 Ú 12 6w1 + 3w2 Ú 12 w1, w2 Ú 0 and point w102 = 13, 12.
The following plot shows several feasible points in a linear program and contours of its objective function.Determine whether each of the following sequences of solutions could have been one followed by an interior point algorithm applied to the corresponding standard-form LP.(a) P1,P5,P6 (b)
Determine whether each of the following is an interior point solution to the standard-form LP constraints 4x1 + 1x3 = 13 5x1 + 5x2 = 15 x1, x2, x3 Ú 0(a) x = 13, 0, 12(b) x = 12, 1, 52(c) x = 11, 2, 92(d) x = 15, 1, 12(e) x = 12, 2, 12(f) x = 10, 3, 132
Write all conditions that a feasible directionw must satisfy at any interior point solution to each of the following standard-form systems of LP constraints.(a) 2w1 + 3w2 - 3w3 = 5 4w1 - 1w2 + 1w3 = 3 w1, w2, w3 Ú 0(b) 11w1 + 2w2 - 1w3 = 8 2w1 - 7w2 + 4w3 = -7 w1, w2, w3 Ú 0
Table 7.4 shows several constraint matrices A (or At) of standard-form LPs and the corresponding projection matrices P (or Pt). Use these results to compute the feasible direction for the specifed equality constraints that is nearest to the given directiond, and verify that the result satisfies
Consider the standard-form LP min 14z1 + 3z2 + 5z3 s.t. 2z1 - z3 = 1 z1 + z2 = 1 z1, z2, z3 Ú 0(a) Determine the direction of most rapid objective function improvement at any solution z.(b) Compute the projection matrix P for the main equality constraints.(c) Apply your P to project the direction
Do Exercise 7-7 for max 5z1 - 2z2 + 3z3 s.t. z1 + z3 = 4 2z2 = 12 z1, z2, z3 Ú 0
An interior point search using scaling has reached current solution x172 = 12, 5, 1, 92.Compute the affine scaled y that would correspond to each of the following x’s.(a) (1, 1, 1, 1)(b) (2, 1, 4, 3)(c) (3, 5, 1, 6)(d) (3, 5, 1, 7)
Do Exercise 7-9 taking the listed vectors as scaled y’s and computing the corresponding x.
Consider the standard-form LP min 2x1 + 3x2 + 5x3 s.t. 2x1 + 5x2 + 3x3 = 12 x1, x2, x3 Ú 0 with current interior point solution x132 = 12, 1, 12.(a) Sketch the feasible space in a diagram like Figure 7.4(a) and identify both the current solution and an optimal extreme point.(b) Sketch the
Do Exercise 7-11 using the LP max 6x1 + 1x2 + 2x3 s.t. x1 + x2 + 5x3 = 18 x1, x2, x3 Ú 0 and current solution x132 = 16, 7, 12.
Return to the LP of Exercise 7-11.(a) Compute in both x and y space the next move direction that would be pursued by affine scaling Algorithm 7A.(b) Verify that the x of part (a) is both improving and feasible.(c) Compute the step size l that Algorithm 7A would apply to your move directions in
Do Exercise 7-13 on the LP of Exercise 7-12.

Showing 3200 - 3300 of 4739

First
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Last

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved