Use the two – phase simplex method Minimize Ζ = 3x1 + 2x2 + x3 Subject to x1 + 4x2 + 3x3 ≥ 50 2x1 + x2 + x3 ≥ 30 −3x1 − 2x2 – x3 ≤ −40 X1 , x2 , x3 ≥ 0
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Use the two – phase simplex method
Minimize Ζ = 3x1 + 2x2 + x3
Subject to x1 + 4x2 + 3x3 ≥ 50
2x1 + x2 + x3 ≥ 30
−3x1 − 2x2 – x3 ≤ −40
X1 , x2 , x3 ≥ 0
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- You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).Solve using Simplex MethodMaximize z = 4x1 + 3x2subject to-x1 +2x2 ≤43x1 +2x2 ≤14x1 – x2 ≤ 3x1, x2 ≥ 0Minimization function is Z=8x1+12x2Subject to: 5x1+2x2≥204x1+3x2≥24X2≥2
- a. Maximize Z = 6X1 + 18X2+20X3 (Don't use excel shortcut solve manually by Simplex LPP method)Sub toX1 + X2 +X3 = 6010X1 +15X2 +20X3 = 9002X1 + 3X2 +3X3≤100And X1, X2, X3 >=0Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm: Maximize Z= 1X1+1X2 Subject to: 2X1+1X2≤72 (C1) 1X1+2X2≤72 (C2) X1,X2≥0Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. Maximize f = 8x + 9y + 3z subject to 2x + 7y + 8z ≤ 100 6x + 3y + z ≤ 160 3x + 4y + 9z ≤ 10 .
- Use the simplex method to maximize the given function. Assume all variables are nonnegative.Maximize f = 3x + 22y subject to 14x + 7y ≤ 35 5x + 5y ≤ 50 (x,y)= f=Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. a) Maximize z = 4x1 + 2x2 Subject to: 2x1 - x2 ≤ 2 3x1 - 4x2 ≤ 8 x1, x2 ≥ 0b) Maximize z = 3x1 + 2x2 Subject to: 4x1 - x2 ≤ 8 4x1 + 3x2 ≤ 12 4x1 + x2 ≤ 8 x1, x2 ≥ 0The LP relationships that follow were formulated by Richard Martin at the Long Beach Chemical Company. Maximize 4X1+12X1X2+5X3 Subject to: 2X1X2+2X3≤70 (C1) 10.9X1−4X2≥15.6 (C2) 10X1+3X2+3X3≥21 (C3) 16X2−13X3=17 (C4) −4X1−X2+4X3=5 (C5) 7X1+2X2+3X3≤80 (C6) For an LP, the objective function developed by Richard is (valid or onvalid) . Constraint C1 is a(n) (valid or onvalid) LP constraint. Constraint C2 is a(n) (valid or onvalid) LP constraint. Constraint C3 is a(n) (valid or onvalid) LP constraint. Constraint C4 is a(n) (valid or onvalid) LP constraint. Constraint C5 is a(n) (valid or onvalid) LP constraint. Constraint C6 is a(n) (valid or onvalid) LP constraint.
- 4. What is the optimized Z value for this following LP problem? Minimize Z= 3x + 10y, subject to (1) 2x + 4y ≤ 12 and (2) 5x + 2y ≥ 10 and (3) x, y ≥ 0. Answer: ______________Minimize Z= x1+2x2-3x3-2x4 subject to: x1+2x2-3x3+x4=4 x1+2x2+x3+2x4=4 x1, x2, x3,x4 are equal or greater then zeroConsider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm: Maximize Z= 1X1+1X2 Subject to: 2X1+1X2≤100 (C1) 1X1+2X2≤100 (C2) X1,X2≥0 Part 2 The optimum solution is: Part 3 X1= ______ (round your response to two decimal places).