Solve the optimal solution (if there are any) for the following LP problem using Big-M method. Maximize Z = 3x1 + 7x2-3x3 Subject to 2x15x2 + 4x3 = 10 x1 + x2 + x3 ≤ 17 5x1 + 8x2 + 9x3 ≥ 10 x1 ≥ 0, x2 ≥ 0, x3 ≥ 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 0Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 10x + 6y + 9z subject to 9x + 11y + 18z ≥ 69 12x + 14y + 4z ≥ 138 and x ≥ 0, y ≥ 0. a- What is the optimal value of x? b-What is the optimal value of y? c- What is the optimal value of z? d- What is the minimum value of the objective function?Graph the following systems of linear Inequalities, shade the solution/feasible region and indicate if solution/feasible region is bounded or unbounded Sy-3x <3 (3y 2 x+3 10 1. 8 2 2. 8 10 -10 -8 -6 -4 -2 -2 46 -4 -6 -8 -10
- Q1 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 0Consider 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…Solve these problems using graphical linear programming and answer the questions that follow. Usesimultaneous equations to determine the optimal values of the decision variables.a. Maximize Z = 4x1 + 3x2Subject toMaterial 6x1 + 4x2 ≤ 48 lbLabor 4x1 + 8x2 ≤ 80 hrx1, x2 ≥ 0 b. Maximize Z = 2x1 + 10x2Subject toDurability 10x1 + 4x2 ≥ 40 wkStrength 1x1 + 6x2 ≥ 24 psi Time 1x1 + 2x2 ≤ 14 hrx1, x2 ≥ 0 c. Maximize Z = 6A + 3B (revenue)Subject toMaterial 20A+ 6B ≤ 600 lbMachinery 25A+ 20B ≤ 1,000 hr Labor 20A+ 30B ≤ 1,200 hrA, B ≥ 0 (1) What are the optimal values of the decision variables and Z?
- Solve 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 ≥ 0Long-Life Insurance has developed a linear model that it uses to determine the amount of term life Insurance a family of four should have, based on the current age of the head of the household. The equation is: y=150 -0.10x where y= Insurance needed ($000) x = Current age of head of household b. Use the equation to determine the amount of term life Insurance to recommend for a family of four of the head of the household is 40 years old. (Round your answer to 2 decimal places.) Amount of term life insurance thousandsWhat combination of x and y will yield the optimum for this problem? Maximize Z = $3x + $15y Subject to: Multiple Choice x= 0, y=4 x= 0, y=3 x= 0, y=0 x= 2y=0 O x=1,y=25 2x + 4y ≤ 12 5x + 2y ≤ 10
- . 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 بالـؤالCombined-cycle power plants use two combustion turbines to produce electricity. Heat from the first turbine’s exhaust is captured to heat waterand produce steam sent to a second steam turbine that generates additional electricity. A 968-megawatt combined-cycle gas fired plant can be purchased for $450 million, has no salvage value, and produces a net cash flow(revenues less expenses) of $50 million per year over its expected 30-year life. Solve, a. If the hurdle rate (MARR) is 12% per year, how profitable an investment is this power plant? b. What is the simple payback period for the plant? Is this investment acceptable?Find the dual of the problem.