Use the simplex method to find the optimal solutions of the following LP Problem. Max. Z = 7x1 + 5x2 subject to x1 + 2x2 ≤ 6 4x1 + 3x2 ≤ 12 x1, x2 ≥ 0
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- Solve the following problem using Simplex Method and find the P value. Maximize: P = 3x + 4y subject to: x+ y 0Q1 Find the best solution for the following model using simplex MAX Z = 10X1 + 8X2 SUB TO: 4X1 + 2X2 < 80 X1 + 2X2 < 50 X1 2 0,X2 2 0Which 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
- . Consider the following linear programming problem: Maximize 12X + 10Y Subject to: 4X + 3Y = 480 2X + 3Y 360 all variables 20 Which of the following points (X,Y) is not feasible? a (70,70) b. (20,90) c. (100,10) d. (0,100) كلا أجرب الأرقام بالـؤالUse the simplex method to find the optimal solution. Assume all variables are nonnegative. Minimize f = 7x + 9y subject to the following constraints. x2 5 y ≤ 19 -x + y 2 2 X = y = f= Need Help? Submit Answer xxx Read ItAnalyze 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 ≥ 0
- Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm: Maximize Z= 1X₁ + 1x₂ Subject to: 2X₁ + 1X₂ ≤60 (C₁) 1X₁ + 2X₂ ≤60 (C₂) X₁ X₂ 20 On the graph on right, constraints C, and C₂ have been plotted. a) Using the point drawing tool, plot all the corner points for the feasible area. The optimum solution is: X₁ = (round your response to two decimal places). (round your response to two decimal places). X₂ = Optimal solution value Z = (round your response to two decimal places). b) If a technical breakthrough occurred that raised the profit per unit of X₁ to $3, due to this change, the optimal solution As a result of the technical breakthrough, the optimum solution is: X₁ = (round your response to two decimal places). X₂ = (round your response to two decimal places). Optimal solution value Z = (round your response to two decimal places). c) If the impact of technical breakthrough was incorrectly determined and instead of X₁ profit…Find the optimal solution by the large M method for the min Z=3Xi 2 X2 メ+ 2X20Maximize Z = x₁ + x₂, subject to X₁ X₂ ≤-3 2x₁ + 7x₂ ≤ 4 and x₁ ≥ 0, x₂ ≥ 0.
- minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2Simplex Method Write in normal form and solve by the simplex method, assuming x, to be nonnegative. 1. The owner of a shop producing automobile trailers wishes to determine the best mix for his three products: flat-bed trailers, economy trailers, and luxury trailers. His shop is limited to working 24 days/month on metal- working and 60 days/month on woodworking for these products. The following table indicates production data for the trailers. Usage per unit of trailer Flat-bed Economy Luxury Available resources 1 2 1 24 Metal work days Wood work days Contribution (Rx100) 60 4 6 2 14 13Solve the following Linear Programming model using the graphical method (USING EXCEL){Write the steps of construction} Q1)MaximizeH = x + 3y Objective functionsubject tox + y ≤ 502x + y ≤ 60 x ≥ 0, y ≥ 0