8.1-2.* Use the dual simplex method manually to solve the following problem. Minimize Z= 5 x1 + 2x2 + 4 x3, subject to 3x1 + x2 + 2x3 2 4 бх, + 3х, + 5х, 2 10 and X 2 0, x2 2 0, Xz 2 0.
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- graph the following constraints: x + y <= 60 15x + 30y <= 20 0.9y > = 0.10x x > = (2/3) y Explan in detailMaximization(Don't use excel shortcut solve manually by Simplex LPP method)1) Max Z = 3X1 + 4X2Sub toX1 + X2 ≤ 202X1 + 3X2 ≤ 50And X1, X2 ≥ 0Maximize: 500X1+300X2Subject to: 15X1+5X2≤30010X1+6x2≤240 8X1+12X2≤450 X1≥0,X2≥0
- A blueprint of a gallery with eight rooms, one entrance and thirteen doorways is shown. The gallery is laid out in a grid of three columns and four rows. Some rooms take up more than one row. The left-hand side contains rooms 1 and 2, the middle column rooms 3, 4, 5, and 6, and the right-hand side rooms 7 and 8. The following list contains each doorway and the rooms it connects. Entrance: Room 1 Opening 1: Rooms 1 and 3 Opening 2: Rooms 3 and 7 Opening 3: Rooms 3 and 4 Opening 4: Rooms 1 and 4 Opening 5: Rooms 4 and 7 Opening 6: Rooms 1 and 2 Opening 7: Rooms 4 and 5 Opening 8: Rooms 2 and 5 Opening 9: Rooms 5 and 7 Opening 10: Rooms 5 and 6 Opening 11: Rooms 7 and 8 Opening 12: Rooms 2 and 6 Opening 13: Rooms 6 and 8 A security firm proposed that two-way cameras be installed at some room openings. Each camera has the ability to monitor the two rooms between which the camera is located. For example, if a camera were located at opening number 4, rooms 1 and 4 would be…7. Using the assembly-line balancing procedures for any assembly-line balancing problem, which of the following is most correct? Multiple Choice The theoretical minimum number of workstations is always less than number of workstations actually used. The theoretical minimum number of workstations is sometimes more than number of workstations actually used. The theoretical minimum number of workstations is sometimes less than Y and sometimes more than number of workstations actually used. The theoretical minimum number of workstations is always less than or equal to number of workstations actually used. The theoretical minimum number of workstations is never less than number of workstations actually used.10.6 This optional problem requires knowledge of statistics. Heywood Home Healthcare is evaluating a project with the following net cash flows and probabilities: Time 0 Year 1 Year 2 Year 2 Year 3 Year 4 Prob = 0.2 ($100,000) 20,000 20,000 20,000 20,000 30,000 Prob = 0.6 ($100,000) 30,000 30,000 30,000 30,000 40,000 Prob = 0.2 ($100,000) 40,000 40,000 40,000 40,000 50,000 The year 5 values include salvage value. Heywood’s corporate cost of capital is 10 percent. What is the project’s expected NPV on the basis of the scenario analysis? What is the project’s standard deviation of NPV? Assume that Heywood’s managers judge the project to have lower-than-average risk. Furthermore, the company’s policy is to adjust the corporate cost of capital up or down by 3 percentage points to account for differential risk. Is the project financially attractive?
- 11-19 The Laurenster Corporation needs to set up an assembly line to produce a new product. The following table describes the relationships among the activities that need to be completed for this product to be manufactured. Modified Problem 11-19: Solve the problem, assuming the following data has changed for 3 activities: - Activity A: a = 4; m =7; b =6 - Activity B: a = 6; m = 9; b = 12 - Activity I: a = 4; m = 5; b = 7 Note to correct a textbook typo: Immediate Predecessors for Activity H are: E, F and G a) Develop the project network for this problem. b) Determine the expected duration, variance and standard deviation for each activity. c) Determine ES, EF, LS, LF and slack time for each activity. d) Determine the total project completion time and critical path(s). e) Determine the probability that the project will be completed in 34 days or less. f) Determine the probability that the project will take longer than 29 days or less.Please do not give solution in image format thanku Let xi = 1 if Project i is selected, i = 1,2,3,4,5; and 0 otherwise: Which answer below indicates that if Project 2 is selected, then Project 4 must be selected? Group of answer choices None of the above x2 + x4 = 1 x2 + x4 ≤ 1 x4 ≤ x2 x2 ≤ x4a. Define the Simplex Algorithm b. How does Simplex Algorithm work? c. Solve a Simple Linear Programming Problem using Simplex.
- There is a cake made for the birthday of an analytics professional. Altogether,there are five persons at the party. However, one person, as a trick, has cut thecake into 15 slices with weights (in grams) of 18, 48, 19, 59, 46, 72, 67, 57, 49, 80,50, 69, 10, 48, 83. The goal is to give all of the pieces out in a way that is mostfair Formulate this as an integer program and find a solution via Solver.5) Min C = X1 + X2 + X3(Don't use excel shortcut solve manually by Simplex LPP method)Subject toX1 – 3X2 + 4X3 = 5X1 – 2X2 <= 32X2 + X3 >=0And X1, X2, X3 >= 0MIn 150x+210y s.t. 3.8x+ 1.2y>=22.9 y>=5 y<=13 45X-30Y=255 X,Y>=0 Solve the linear problem graphically (X,Y)=( ) How many extreme points exist for this problem