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- a) What is the optimal solution to this problem? Solve it graphically. b) If a technical breakthrough occurred that raised the profit per unit of X1 to $3, would this affect the optimal solution? c) Instead of an increase in the profit coefficient X1 to $3, suppose that profit was overestimated and should only have been $1.25. Does this change the optimal solution?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 0b) Maximize Z = −40X1 −100X2s.t 10X1 + 5X2 ≤ 2502X1 + 5X2 ≤ 1002X1 + 3X2 ≤ 90X1, X2 ≥ 0Solve by simplex method, what are the solutions? Show that this problem hasmultiple solutions and find the solutions?
- Chapter 6. Solve the following Linear Program using the Solver method and answer the questions given below (round to two decimal places): Maximize 12A + 15B s.t. 3A + 7B <= 250 5A + 2B <= 200 B <= 25 A, B >= 0 a. The optimal value of A is 31.03 and the optimal value of B is 22.41. b. The maximized function yields a solution of 708.62. Chapter 7. For the problem you solved in Q1, obtain the Sensitivity Report, and answer the following questions. Remember to round to two digits and you can enter “infinity” for unlimited regions: The range for Variable A is from ????? to ????? The range for Variable B is from ????? to ????? The range for Constraint 1 is from ????? to ????? The range for Constraint 2 is from ????? to ????? The range for Constraint 3 is from ????? to ?????4. 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.Although the problems say solve graphically, please solve all problems using the QM for Windows software or solve manually. B.6 The Christina Alvarez Company manufactures two lines of designer yard gates, called model A and model B. Every gate requires blending a certain amount of steel and zinc, the company has available a total of 25.000 Ib of steel and 6,000 lb of zinc. Each model A gate requires a mixture of 125 Ib of steel and 20 lb of zinc, and each yields a profit of 590. Each model B gate requires 100 1b of steel and 30 ib of zinc and can be sold for a profit of $70. Find by graphical IP the best production mix of yard gates.
- 1. A specific assignment of values to decision variables is called what? a. Constraint b. Feasible c. Solution d. None of the above 2. Which of the following must be true of a feasible solution a. All of what Solver calls changing variables must be greater than 0 b. It is optimal c. It violates no constraints d. None of the aboveFind the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 11x + 5y + 10z subject to 8x + 12y + 19z ≥ 68 13x + 16y + 5z ≥ 136 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?A decision problem has the following three constraints: 70X + 6Y <= 420; 24X + 3Y= 72; and 11X - Y <= 14 . The objective function is Min 17X + 38Y . The objective function value is : a. 338 b. 676 c. unbounded d. infeasible e. 0
- A goldsmith makes two types of jewelry. A model A ring is made with 1 g of gold and 1.5 g of silver and sells for 25 UM.Another model B ring sells for 30 UM and is made of 1.5 g of gold and 1 g of silver. If you only have 750 gof each metal, how many rings should be made of each type to obtain maximum profit?Requested:- Make Initial Table of the problem.- Obtain the Case Variables- Obtain the Objective Function- Get Restrictions- Create the Simplex Table- Obtain the Optimal Solution and the Slack Variables.Solve this operational research exercise.Optimal solution 4T+3C=240 2T+1C=100 →T=30, C-40 Can you please explain to me the solution and way of how he did get the exact coordinate points in the graph? I know there is a formula or way to calculate since it is hard to find out the exact point when manually plotting a graphGiven 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)?