2. Graph the following system of linear Inequalities, shade the solution/feasible region and indicate if solution/feasible region is bounded or unbounded x + y<9 2x + 5y > 10 X20; y>0
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- Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 14x + 7y + 8z subject to 6x + 12y + 19z ≥ 64 17x + 24y + 9z ≥ 128 and x ≥ 0, y ≥ 0, z ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the optimal value of z? What is the minimum value of the objective function?Find the indicated maximum or minimum value of the objective function in the linear programming problem. Minimize g = 10x + 6y subject to the following. x + 2y ≥ 10 2x + y ≥ 11 x + y ≥ 9 x ≥ 0, y ≥ 0
- Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative.Maximize f = 5x + 9y subject to 8x + 5y ≤ 200 x + 6y ≤ 250. x y s1 s2 f first constraint second constraint objective functionFind the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = 14x + 13y + 5z subject to 9x + 11y + 18z ≤ 61 14x + 15y + 12z ≤ 122 and x ≥ 0, y ≥ 0, z ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the optimal value of z? What is the maximum value of the objective function?The standard form of the following linear programming model is given. Find the values of variables at the point of intersection of constraint 1 and the vertical axis (y). (Round your answers to 3 decimal places.) Maximize P = 30x + 15y + 0s1 + 0s2 subject to 6x + 12y + s1 = 19 13x + 12y + s2 = 35 and x, y, s1, s2≥ 0.
- Given this linear programming model, solve the model and then answer the questions that follow.Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc.Subject toMachine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hoursMaterials 2x1 + 2x2 + 4x3 ≤ 200 poundsProduct 2 x2 ≤ 16 units x1, x2, x3 ≥ 0 a. Are any constraints binding? If so, which one(s)?Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 17x + 19y subject to 8x + 14y ≥ 21 11x + 6y ≥ 31 and x ≥ 0, y ≥ 0. What is the optimal value of x and y? What is the minimum value of the objective function? Please show me step by step how to do this by hand, not through excel.Consider the following LP problem: Min 6X+ 27Y Subject to : 2 X + 9Y => 25, and X + Y <= 75. Pick a suitable statement for this problem: a. X=37.5, Y=37.5 is the only optimal solution. b. Optimal Obj. function value is 75 c. X = 0, Y = 0 is the only optimal solution. d. Optimal Obj. function value is 0
- Consider the following linear programming model with 4 regular constraints:Maximize 3X + 5Y (a) Draw your graph in the space below:subject to: 4X + 4Y ≤ 48 (constraint #1) 4X + 3Y ≤ 50 (constraint #2) 2X + 1Y ≤ 20 (constraint #3) X ≥ 2 (constraint #4) X, Y ≥ 0 (non-negativity constraints)(a) Which of the constraints is redundant? Constraint #______.Justify by drawing a graph similar to Figure 7.14 on p.263.(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints).Constraint #1: _______________________________________________________________Constraint #2: _______________________________________________________________Constraint #3: _______________________________________________________________Constraint #4: ______________________________________________________________Solve the following Linear programming problem using the simplex method:Maximize Z = 10X1 + 15X2 + 20X3subject to:2X1 + 4X2 + 6X3 ≤ 243X1 + 9X2 + 6X3 ≤ 30X1, X2 and X3 ≥ 0(b) Suppose X1, X2, X3 in (a) refer to number of red, blue, and green balloons respectivelywhich are produced by a company per day. And Z is the total profit obtained afterselling these balloons. Interpret your answer obtained in (a) above(c) Write the dual of the following linear programming problem:Minimize Z = 2X1 − 3X2 + 4X3subject to:3X1 + 4X2 + 5X3 ≥ 96X1 + X2 + 3X3 ≥ 47X1 − 2X2 − X3 ≤ 105x1 − 2X2 + X3 ≥ 34X1 + 6X2 − 2X3 ≥ 3X1, X2 and X3 ≥ 04. Consider the following linear programming problem: Maximize Z=$15x + $5y, subject to (1) 2x + y ≤ 10 and (2) 4x + 3y ≤ 24 and (3) x, y ≥ 0. Will the optimal solution change if the objective function becomes Maximize Z=$15x + $20y (constraints remain the same)? Select one: a. Can't determine given the information. b. Yes, it will change. c. No, it remains the same.