Consider the following all-integer linear program.5Xq + 8X26x₁ + 5x₂ ≤ 3510x₁ + 4x₂ ≤ 401x1 + 2x₂ ≤ 12X₁, X₂ ≥ 0 and integer(a) Graph the constraints for this problem. Use points to indicate all feasible integer solutions.X2X28Maxs.t.224at (x₁, x₂)=68(c) Find the optimal integer solution.at (x₁, x₂)X184(b) Find the optimal solution to the LP Relaxation. (Round your answers to three decimal places.)at (x₁, x₂)Using this solution, round down to find a feasible integer solution.2Is it the same as the solution obtained in part (b) by rounding down?YesNo468iX286422468X1X28422468X1

Objective Functions and Constraints:Objective Function:Constraints:Subject to

Answered: Consider the following all-integer…

Practical Management Science

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Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Q1: convert the following form primal to dual MIN Zx = X1 + 2 X2 subject to 2 X1 + 4 X2 ≤ 160 3 X1 - X2 = 30 4 X1 ≥ 10 and X1,X2≥0;
Estimate a range for the optimal objective value for the following LPs: *(a) Minimize z = 5x₁ + 2x₂ subject to (b) Maximize z subject to x₁ + 5x₂ + 3x3 X₁ X₂ ≥ 3 2x₁ + 3x₂ = 5 X1, X₂ ≥ 0 x₁ + 2x₂ + x3 = 30 2x₁ - x₂ = 40 X1, X2, X3 ≥ 0
b) The figure below presents an unbounded feasible region of a five constrained LP problem. 10- |(0, 6) 6. (1, 4) 4 (3, 2) 2+ (9, 0) 8 10 i. Write down in terms of x and y the inequalities that represent these constraints. ii. If the objective function is Z = 0.12x + 0.15y, determine the optimal solution to this problem (show the movement of the isocost line). ii. Identify the binding and non-binding constraints.
1
4a) Convert the following problem to Standard Form. max z := -2x1 + x2 s.t. 2x1 + x2 1 x1 > 0, x2 free. 4b) Write the augmented form of the following standard form problem. max z := 4.x1 – 25x2 x1,x2,x3,x4 s.t. x1 – x3 = 5 X2 – x3 + x4 = 0 x > 0
Answer the next TWO (2) questions using the following linear programming problem and the corresponding graphical solution: Max subject to Z=30 x₁ +20 x₂ 2 x₁ + 2x₂ ≤8 8 x₁ +4x2 ≤24 X₂ 2 (constraint I) (constraint II) 13. What is the upper bound of the sensitivity range for the coefficient of x₁ in the objective function? a. 60 b. 10 c. 40 d. 20 14. What is the upper bound of the sensitivity range for the Right-Hand Side (RHS) of constraint I? a. 8 b. 12 c. 4 d. 6
Example 14c 1.plot all the corner points for the feasible area. 2. Find the optimum solution to X= Y= VALUE Z=
Variable Cells Model Variable Constraints E S D Constraint Number 1 E 2 3 S D S D Name Economy Models Standard Models Deluxe Models Name Total Profit: $ Fan Motors Cooling Coils Manufacturing Time Optimal Solution Constraints Fan motors Cooling coils Final Value 80.000 120.000 0.000 Final Value 200.000 320.000 2080.000 a. Identify the range of optimality for each objective function coefficient. If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place. Objective Coefficient Range Variable lower limit upper limit E Reduced Cost 0.000 0.000 -24.000 Manufacturing time. AUTO Shadow Price 31.000 32.000 0.000 Right-Hand-Side-Range lower limit upper limit Objective Coefficient 63.000 95.000 135.000 b. Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal…

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Consider the following all-integer linear program. 5xy + 8x2 Max s.t. 6x₁ + 5x₂ ≤ 35 10x₂ + 4x₂ ≤ 40 1x₁ + 2x₂ ≤ 12 X₁ X₂20 and integer (a) Graph the constraints for this problem. Use points to indicate all feasible integer solutions. X₂