What special case in linear programming does the following graph depict? 10 X2 8 2 0 2x₁+x₂57 2 A) infeasibility x1 + x₂ 28 C) objectivity 4 B multiple optimal solutions X₁ (D unboundedness 10
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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 ≥ 0For the products A, B, C, and D, which of the following could be a linear programming objective function? Select one: a. Z = 1A + 2BC + 3D b. Z = 1A + 2AB + 3ABC + 4ABCD c. Z = 1A + 2B + 3C + 4D d. Z = 1A + 2B/C + 3D
- Vladimir Ulanowsky is playing Keith Smithson in atwo-game chess match. Winning a game scores 1 match 19.4 Further Examples of Probabilistic Dynamic Programming Formulations 1029 point, and drawing a game scores 12match point. After thetwo games are played, the player with more match points isdeclared the champion. If the two players are tied after twogames, they continue playing until someone wins a game(the winner of that game will be the champion). Duringeach game, Ulanowsky can play one of two ways: boldly orconservatively. If he plays boldly, he has a 45% chance ofwinning the game and a 55% chance of losing the game. Ifhe plays conservatively, he has a 90% chance of drawing thegame and a 10% chance of losing the game. Ulanowsky’sgoal is to maximize his probability of winning the match.Use dynamic programming to help him accomplish thisgoal. If this problem is solved correctly, even thoughUlanowsky is the inferior player, his chance of winning the match is over 12. Explain this…Consider 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≥0Consider the following LP:Maximize z = 16x1 + 15x2subject to40x1 + 31x2 <=124-x1 + x2<= 1x1<=3x1, x2 >= 0(a) Solve the problem by the simplex method, where the entering variable is thenonbasic variable with the most negative z-row coefficient.
- Consider 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).Set 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 .Which of the following is the optimal value of the objective function for the LP model in this problem? Minimize z=4x + 8y Subject to: x+1.6y>=45 2x+0.5y>=40 X+y<=40 XY>=0 a.220 b.160 c.240 d.200
- Solve Maximize: Z = 4X1 + 3X2 + 9X3 Subject to: 2X1 + 4X2 + 6X3 ≥ 15 6X1 + X2 + 6X3 ≥ 12 X1, X2, X3 ≥ 0 Use simplex method.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 ≥ 0A matrix is said to be upper triangular if for i > j, aij=0. Show that the determinant of any upper triangular 3* 3matrix is equal to the product of the matrix’s diagonalelements. (This result is true for any upper triangular matrix.)