Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = subject to and 18x + 23y + 10z 14x + 16y + 23z ≤ 56 9x + 8y + 7z ≤ 112 x 28, y 28, z 20. 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 maximum value of the objective function? Maximum value
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- Simplex Method Solve the following LP problem using the simplex method. Maximize: P = 9x + 7ySubject to:2x + y ≤ 40 x + 3y ≤ 30x, y ≥ 0 What is the entering variable and leaving variable in Table 1? Choices: A. Entering Variable: y and Leaving Variable: S1 B. Entering Variable: x and Leaving Variable: S1 C. Entering Variable: x and Leaving Variable: S2 D. Entering Variable: y and Leaving Variable: S23. A company produces three products: A,B and C. Each product requires two raw materials; steel and aluminum. The following LP model describes the company’s product mix problem x1, x2, and x3 represent the number of units of product A, B and C respectivelyMax Z = 30x1 + 10x2 + 50x3Subject to6 x1+ 3 x2 + 5 x3 ≤ 450 (steel)3 x1 + 4 x2+ 5 x3 ≤ 300 (alumimium), X1, x2, x3 ≥ 0 Identify the two production methods that optimize the company’s profit (hint: Use simplex method)21. A linear programming problem has two constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is TRUE? Part 2 A. The graphical origin (0, 0) is not in the feasible region. B. The feasible region includes all points that satisfy one constraint, the other, or both. C. The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized. D. The two corner points are (0, 0) and (50, 12.5). E. There are four corner points including (50, 0) and (0, 12.5)
- 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 0Simplex Method Solve the following LP problem using the simplex method. Maximize: P = 9x + 7ySubject to:2x + y ≤ 40x + 3y ≤ 30x, y ≥ 0 What is the entering variable and leaving variable in Table 2? a. Entering Variable: x and Leaving Variable: S2 b. Entering Variable: y and Leaving Variable: S2 c. Entering Variable: y and Leaving Variable: S1 d. Entering Variable: x and Leaving Variable: S1b) 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?
- Show the complete Linear Programming Model. Show solutions (i.e. decision variables, objective function, subject to constraints, etc.) Q. A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running, at least three tons of ore must be processed each day. Ore from source A costs $1,000 per ton to process, and ore from source B costs $500 per ton to process. Costs must be kept to less than $4,000 per day. Moreover, Government Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints? Formulate the LP model.22. Suppose that the feasible region of a maximization LP problem has corners of (0,0), (10,0), (5,5), and (0,7). If profit is given to be $X + $3Y what is the maximum profit the company can earn? Part 2 A. $10 B. $0 C. $14 D. $21 E. $15Chapter 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 ?????
- Problem 3: Let L(x, y) be the statement “x loves y”, where the domain for both x and y consists of all people in the world. Use quantifiers to express each of the following statements.1. Everybody loves Jerry.2. Everybody loves somebody.3. There is somebody whom everybody loves.4. Nobody loves everybody.5. There is somebody whom Lydia does not love.6. There is somebody whom no one loves.7. There is exactly one person whom everybody loves.8. There are exactly two people whom Lynn loves.9. Everybody loves himself or herself.10. There is someone who loves no one besides himself or herself.Please do not give solution in image format thanku Consider the following set of constraints (Maximization problem): 10X+ 20y>= 43, and 30X+ 10Y >= 21.5. The following is true for this problem: a. Infeasible problem b. Unbounded problem c. X=0, Y=10 is the optimal solution d. X=10, Y=16 is the optimal solution. 2. Consider the following LP problem: Min 12X+ 12Y; Subject to ; 4 X + 4Y <= 31, and X + Y <= 93. Which one of the following is true: a. Optimal objective function value is O. b. Optimal objective function value is 93. c. Slack for each constraint is 0. d. X-46.5, Y=46.5 is the optimal solutionSet up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. Maximize f = 8x + 9y + 3z subject to 2x + 7y + 8z ≤ 100 6x + 3y + z ≤ 160 3x + 4y + 9z ≤ 10 .