The linear system o equation of 4. 3. X3 2. has an exact solution À= (,21-) Find the optimal choice of 2. successive over- Belaxati SOR) method with two significant compute the first approximation using the SOR methad digits ronding two
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- 7. Use Lagrange multipliers to give an alternate solution. Find two positive numbers whose product is 100 and whose sum is a minimum.Don't use chatgpt, I will 5 upvotes Please solve the following set of equations using Gauss Jordan Method: 2x1+x2+x3+3x4+2x5=-2 x1+2x2+2x3+x4+x5=4 x1+2x2+9x3+x4+5x5=3 3x1+x2+x3+7x4+x5=-5 2x1+x2+5x3+x4+8x5=1Min Z = 12X1 + 18X2 + 8X3 5X1 + 8X2 +9X2 >= 18 9X1 + 15X2 + 12X3 >= 36 10X1 + 15X2 + 12X3 >= 45 X1, X2, X3 >= 0Look for the Optimal Solution
- can you please show an easy way using d’Alembert's reduction of order method to find a second linearlyindependent solution. What is the general solution of the diferentialequation for number 7Express In(y-C1 ) =C2 +Inx Use Least Square Method. having these points. (2,5),(3,1),(5,2),(6,0) and 7,1).Max Z = 3X1 + 2X2Subject to:X1 + 2X2 <= 62X1 + X2 <= 8-X1 + X2 <= 10X1 + X2 <= 2X1, X2 >=0a) Find the optimal solution of the duality using the Big M method
- Consider the problem (attached image) min x2 subject to x2 = 1 x1, x2 ≥ 0 Write down its dual. For both the primal and the dual problem determine whether they have unique optimal solutions and whether they have nondegeneration optimal solutions.Although the Hungarian method is an efficient methodfor solving an assignment problem, the branch-and-boundmethod can also be used to solve an assignment problem.Suppose a company has five factories and five warehouses.Each factory’s requirements must be met by a singlewarehouse, and each warehouse can be assigned to only onefactory. The costs of assigning a warehouse to meet afactory’s demand (in thousands) are shown in Table 77.Let xij 1 if warehouse i is assigned to factory j and 0otherwise. Begin by branching on the warehouse assigned tofactory 1. This creates the following five branches: x11 1,x21 1, x31 1, x41 1, and x51 1. How can we obtaina lower bound on the total cost associated with a branch?Examine the branch x21 1. If x21 1, no furtherassignments can come from row 2 or column 1 of the costmatrix. In determining the factory to which each of theunassigned warehouses (1, 3, 4, and 5) is assigned, we cannotdo better than assign each to the smallest cost in…1. Max Z = 25X1 + 35X2 + 80X3 2X1 + 5X2 + 3X3 <= 40 6X1 + 12X2 + 8X3 <= 48 7X1 + 15X2 + 9X3 <= 75 X1, X2, X3 >= 0 Look for the Optimal Solution 2. Min Z = 12X1 + 18X2 + 8X3 5X1 + 8X2 +9X2 >= 18 9X1 + 15X2 + 12X3 >= 36 10X1 + 15X2 + 12X3 >= 45 X1, X2, X3 >= 0Look for the Optimal Solution
- Assume that you are located at (A) which is New Orleans. Let Boston (B), Chicago (C) , Denver (D), and El Paso (E) represent four cities. Use the Brute Force Method to find the optimal solution to visiting each of the cities and returning home. Use the Nearest Neighbor Method to approximate the optimal solution. Identify how much money is being saved by using the optimal solution instead of the approximation.In 2015, the Phoenix/Zweig Advisors Zweig Total Return fund (ZTR) was expected to yield 5% and the Madison Asset Management Madison Strategic Sector Premium fund (MSP) was expected to yield 7%. You would like to invest a total of up to $60,000 and earn at least $3,500 in interest. Draw the feasible region that shows how much money you can invest in each fund (based on the given yields). Find the corner points of the region. Make sure you use a test point in your work. Shade the region(s) that is NOT the solution and label the region SOLUTION SET.we are going to use linear programming to develop a simple machinelearning algorithm to help us classify data points. Training data and Test data.Each of the 20 data points in the training data consists of 2 sensor readings x1, x2 whichare real numbers corresponding to the readout of two sensors during an event and a classi- cation y which is either 0 or 1, 0 indicates the event corresponding to the sensor data wasdetermined to not be a gravitational wave and a 1 indicates the event was determined tobe a gravitational wave. Thus, a typical line in the le looks something like:0.0 78.1 60.6Which indicates the 2 sensors had readings 78.1, 60.6 respectively, and the 0.0 indicatesno gravitational wave was observed. The test data consists again of sensor readings xi but with no classi cation y provided.Your job is to use the training data to develop a model that can take in sensor data andpredict the classi cation (again, 0 or 1). You will then run your model on the 20 points inthe test…