3. Consider the balanced transportation tableau Destinations 1 3 4 Si 2 3 6. 12 5 4 8 10 9. Basic Cell Sources 9. 3. 11 15 7 4. 4 6. 8 3 4 6. d; 6. 3 8 (a) Find the solution corresponding to the indicated basic cells. (b) Is the solution found in part (a) optimal? If not, find the optimal solution. mablom i:. ...L: in 1.
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- Let x = pieces of sofa, Y=pieces of table, Z=pieces of chair1.What is the objective function?2. Express the first constraint (wood) in mathematical sentence3. Express the second constraint (upholstery) in mathemathical sentence.4. Express the third constraint (Labor) in mathemathical sentence1. Consider the following transportation tableau with three origins and three destinations. To From Windhoek Gobabis Walvis Bay Supply Rundu 4 10 6 100 Oshakati 8 16 6 300 Katima Mulilo 14 18 10 300 Demand 200 300 200 Required Marks Sub total Total Use the Vogel Approximation method (VAM) to find an initial feasible solution? 20 20 ToFor the linear program Max 2A + 3Bs.t. 1A + 2B <= 6 5A +3B <= 15 A, B >= 0 find the optimal solution using excel. What is the value of theobjective function at the optimal solution?
- Given the following information for a product-mix problem with three products and three resources. Primal Decision Variables: x1 = number of unit 1 produced; x2 = # of unit 2 produced; x3 = # of unit 3 produced Primal Formulation:Dual Formulation: Max Z (Rev.) = 25x1 + 30x2 + 20x3Min W = 50π1+ 20π2+25π3 Subject To8x1+ 6x2+ x3≤ 50(Res. 1 constraint)Subject To8π1+ 4π2+2π3≥ 25 4x1+ 2x2+ 3x3≤ 20(Res. 2 constraint)6π1+ 2π2+π3 ≥ 30 2x1+ x2+ 2x3≤ 25(Res. 3 constraint)π1+ 3π2+2π3≥ 20 x1, x2, x3≥ 0 (Nonnegativity)π1, π2, π3 ≥ 0 Optimal Solution: Optimal Z = Revenue = $268.75 x1 = 0 (Number of unit 1)Dual Var. Optimal Value = 22.5 (Surplus variable in 1st dual constraint) x2 = 8.125 (Number of unit 2)Dual Var. Optimal Value = 0 (Surplus variable in 2nd dual constraint) x3 = 1.25 (Number of unit 3)Dual Var. Optimal Value = 0 (Surplus variable in 3rd dual constraint) Resource Constraints: Resource 1 = 0 leftover…Maximize z= 5R+8P Subject to R+3/2P≤900 1/2R+1/3P≤300 1/8R+1/4P≤100 R,P ≥ 0 non-binding constraint: R+(3/2) P≤900 binding constraints: (1/8) R+(1/4) P≤100 and (1/2) R+(1/3) P≤300 redundant constraint R+(3/2) P≤900 1. What is the range of the coeficient, c1, of the decision variable R that will make the optimal solution remain unchange? a. 13/3≤c1≤7 b. 10/3≤c1≤10 c. 4≤c1≤12 d. 13/2≤c1≤19/2 2. What is the range of the coeficient, c2, of the decision variable P that will make the optimal solution remain unchange? a. 13/3≤c1≤7 b. 10/3≤c1≤10 c. 4≤c1≤12 d. 13/2≤c1≤19/2Problem 7-17 (pg 279) Using the following equations, graph the constraints and solve using the corner point approach ONLY. X1 = number of benches produced X2 = number of tables produced Maximize profit = $9X1 + $20X2 subject to 4X1 + 6X2 <= 1,200 hours 10X1 + 35X2 <= 3,500 feet X1, X2 >= 0
- For the linear program Max 2A+3B s.t 1A+2B≤6 5A+3B≤15 A,B≥0 Find the optimal solution using the graphical solution procedure. What is the value of the object function at the optimal solution?Consider the followingg linear programming problem: Max 3A + 3Bst. 2A + 4B ≤ 12 6A + 4B ≤ 24 A, B ≥ 0 The point (0.0,0.0) is: a. infeasible. b. is one of the extreme points. c. the optimal solution. d. unboundedMax −A + 2B s.t. -2A + 3B ≤ 8 (Constraint 1) 6A - 2B ≤ 5 (Constraint 2) A + B ≤ 5 (Constraint 3) A ≥ 1 (Constraint 4) A, B ≥ 0 SHOW ALL CALCULATION STEPS a) Solve the LP Model using the graphical method. Label your graph completely (and upload your graph as a jpg). State your optimal solution and objective function value. b) Calculate the Slack/Surplus for each constraint. c) Calculate the Shadow/dual Prices for each constraint.
- Variable cells Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease $B$6 Activity 1 3 0 30 23 17 $C$6 Activity 2 6 0 40 50 10 $D$6 Activity 3 0 –7 20 7 1E+30 Constraints Cell Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease $E$2 Resource A 20 7.78 20 10 12.5 $E$3 Resource B 30 6 30 50 10 $E$4 Resource C 18 0 40 1E+30 22 What is the optimal objective function value for this problem?A Manager has the problem of assigning four new machines to three production facilities.The respective profits derived are as shown. If only one machine is assigned to a productionfacility, determine the optimal assignment.Profits ($’000) production facilityMachine A B CA 10 10 14B 10 11 13C 12 10 10D 13 12 11(c) Use Simplex method toMaximize 1 2 Ζ = 4x +10xSubject to 1 2 2x + x ≤ 501 2 2x + 5x ≤1001 2 2x + 3x ≤ 901 2 x , x ≥ 0QUESTION TWO#1- Maxwell Manufacturing makes two models of felt tip marking pens. Requirements and available resources for each lot of pens are given in the following table: Fliptop Model Tiptop Model Available Plastic 3 4 36 Ink Assembly 5 4 40 Molding Time 5 2 30 The profit for either model is $1,000 per lot. a) What is the linear programming model for this problem? b) Using Microsoft Excel's Solver, find the optimal solution. How many Fliptop models and how many Tiptop models should be produced? What is the maximum profit? c) Will there be excess capacity in any resource? Use Excel's Solver and run a sensitivity report to answer the following questions. d) Over which range can the objective function coefficient for Fliptop Models change without affecting the original optimal solution? What is this range called? e) What is the shadow price (dual price) for the plastic constraint and how would you interpret it? f) What is the shadow price (dual price)…