min. of
i have used lagrange multplier method
in which i first took derivative of objective function with respect to x and equated it with derivative of subjected function multiplied by lambda.
Problem 8-02 (Algorithmic) Consider the problem Min 2x2 18X2XY - 18Y58 X 4Y 8 s.t. a....
Problem 8-02 (Algorithmic) Consider the problem 2x18x + 2XY Y- 18Y +53 Min s.t. X 4Y s 8 a. Find the minimum solution to this problem. If required, round your answers to two decimal places. 1.16 V, Y V, for an optimal solution value of 4.36 Optimal solution is X3.36 b. If the right-hand side of the constraint is increased from 8 9, how much do you expect the objective function to change? If required, round your answer to two...
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2 〈 24 1xl t 2x2< 16 And xl, x2> 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of xl, x2, and Z. b) Assume that the objective function coefficient for xl changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective...
MAX X Z = 3X1 + 4x2 s.t 2x1 + 2x2 ≤ 8 1x1 + 2x2 ≤ 6 2x2 ≥ 1 please graph with the optimal solution. Then dual price for the first constraint by adding one. Then dual price for the third constraint adding one. Please also graph these with the same graph showing the new optimal solutions Also please show the iso-z lines for the initial problem.
Problem 3-23 (Algorithmic) Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Shaper Grinder Component 1 4 2 5 3 2 The shaper is available for 130 hours, and the grinder is available for 85 hours. No more than 350 units of component 3 can be sold, but up to 1050 units of each of...
Problem 3-13 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $59, $89, and $137, respectively. The production requirements per unit are as follows: Number of Fans Number of Cooling Coils Manufacturing Time (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 240 fan motors, 380 cooling coils, and 2500 hours of manufacturing...
M 4. Consider the utility maximization problem max U(x,y) = x +y s.t. x + 4y = 100. (a) Using the Lagrange method, find the quantities demanded of the two goods. (b) Suppose income increases from 100 to 101. What is the exact increase in the optimal value of U(x, y)? Compare with the value found in (a) for the Lagrange multiplier. (C) Suppose we change the budget constraint to px + y = m, but keep the same utility...
. Solve the following LP minimization problem. Min 3X + 2Y s.t. 5X + 3Y <= 30 3X + 4Y >= 36 Y >= 7 X , Y >= 0 Group of answer choices X = 0, Y= 9 The optimal value of the objective function is 5. None of the other answers are correct. The optimal value of the objective function is 7. X = 1,...
Consider the following LP problem: Minimize Cost = 3x1 + 2x2 s.t. 1x1 + 2x2 ≤ 12 2x1 + 3 x2 = 12 2 x1 + x2 ≥ 8 x1≥ 0, x2 ≥ 0 A) What is the optimal solution of this LP? Give an explanation. (4,0) (2,3) (0,8) (0,4) (0,6) (3,2) (12,0) B)Which of the following statements are correct for a linear programming which is feasible and not unbounded? 1)All of the above. 2)Only extreme points may be optimal....
Problem 2-10 (Algorithmic) For the linear program Max 3 A + 3 B s.t. A + 3B ≤ 9 10A + 6B ≤ 30 A, B ≥ 0 select the correct graph that identifies the optimal solution. What is the value of the objective function at the optimal solution? (i) BA (ii) BA (iii) BA (iv) BA The value of the objective function at the optimal solution is .
Problem 3-02 (Algorithmic) Consider the following linear program: Max 3A 2B 1A 1B s 12 1A 2B s 20 A, B 2 0 The value of the optimal solution is 31. Spose that the right-hand side of the constraint 1 is increased from 12 to 13. a. Use the graphical solution procedure to find the new optimal solution. 26 Optimal Solahion A6584 2B-325 28-39 20 12-14 16 11 1012 14 1618 nv) B Optimal Solution 23-26 26 30 2 34...