Find the initial Simplex tableau at the start of Phase II with (fixed) row0 at the bottom for the following LP: Minimize z = 1.1 x + 1.4 y s.t. 2x + 4.3 y 4.7 and with 1.2 x + 7.5 y 7.7 x,y > 0 0 0 1 y COM 1 0 0 1 0 0 e1 e2 01 02 || REG 1.530
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- Use two-phase simplex Method to solve the following LP Minimize z= 6 x1 + 3 x2 Subject to x1+x2 ≥ 1 2x1- x2 ≥ 1 3x2 ≤ 2 x1,x2 ≥ 0Consider the LP model and its corresponding graph below. Maximize z = 5x + 4ySubject to:3x + 2y <= 12x + 2y >= 8x >= 0y >= 0 From the given graph, what are the corner points of the feasible region? What are the values of x and y for the optimal solution? What is the maximum value of z?Question 3:Using Lagrangian Multiplier Method, maximize the following utility function: U=2x+3y+ 3xySubject theto following constraint:2x+3y = 8and find out optimal values of goods 'x' and 'y', where utility of the isconsumer maximum?
- 3. If you want to design a pop can to hold 350 cm3 of pop using the least amount of metal to make the can, what would you use for f and g in the Lagrange Multiplier Method?consider the transportation problem presented in the following table: D1 D2 D3 D4 SUPPLY S1 19 30 50 10 7 S2 70 30 40 60 9 S3 40 8 70 20 18 Demand D5 8 7 14 find initial feasible solution using Vogel's Approximation method (VAM), also find optimal solution using stepping-stone method.Suppose that in a certain year, the Phoenix/Zweig Advisors Zweig Total Return fund (ZTR) was expected to yield 4%, and the Madison Asset Management Madison Strategic Sector Premium fund (MSP) was expected to yield 9%. You would like to invest a total of up to $60,000 and earn at least $4500 in interest. Draw the feasible region that shows how much money you can invest in each fund (based on the given yields). (Place ZTR on the x-axis and MSP on the y-axis.). Find the corner points of the region. (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.) (x, y)= ( ) (x, y)= ( ) (x, y)= ( )
- Use Euler's method with step size 0.25 to compute the approximate y-values y1, y2,y3, and y4 of the solution of the initial-value problem y1= ,y2= ,y3= ,y4=Consider the following problem. Minimize Z=3X1+2X2+4X3 Subject to 2X1+X2+3X3=60 3X1+3X2+5X3≥120 and X1, X2, X3≥0 Using the two-phase method, work through the simplex method to solve the problem2. identify the feasible region and optimal solution for the linear program max z =2x1 + 3x2 s.t 1x1 + 2x2 < 6 5x1 + 3x2 < 15 x1, x2 > 0
- Use the method of Lagrange Multipliers to find the maximum and minimumvaluesof x2+y2 subject to the constraint x4+ y4=2Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint,f(x, y, z) = x^2 + y^2 + z^2; x^4 + y^4 + z^4 = 3A function, z = ax + by, is to be optimized subject to the constraint, x2 + y2=1 where a and b are positive constants. Use Lagrange multipliers to show that this problem has only one solution in the positive quadrant (i.e. in the region x > 0, y > 0) and that the optimal value of z is √a2 +b2.