Q(4)A) What is shadow cost how and to obtained it by LP. B) Consider the following linear program for product mix problem Max $Z = 45X + 80Y$ st. $5X + 20Y \le 400$, $10X + 15Y \le 450$ and $X, Y \ge 0$. Obtained its dual, and solve dual.
Added by Christie B.
Close
Step 1
Step 1: The primal problem is: Max Z=45X+80Y subject to: 5X+20Y≤400, 10X+15Y≤450 X,Y≥ 0. Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 82 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
(H&L 6.1-5.) Consider the following problem: max z = 5x1 + 4x2 + 3x3 subject to x1 + x3 <= 15 (resource 1) x2 + 2x3 <= 25 (resource 2) and x1 >= 0, x2 >= 0, x3 >= 0. (a) Construct the dual problem for this primal problem. (b) Solve the dual problem graphically. Use this solution to identify the shadow prices for the resources in the primal problem. (c) Confirm your results from part (b) by solving the primal problem automatically by the simplex method and then identifying the shadow prices.
Adi S.
Problem 4: (Linear Programming Duality) [20 points] Given the following linear programming problem: max x1 + 2x2 s.t. -2x1 + x2 <= 2 -x1 + 2x2 <= 7 x1 <= 3 x1, x2 >= 0 (a) (5 points) Write down the Dual LP for the provided problem (b) (5 points) Assuming that the optimal solution of the primal problem is: x1 = 3, x2 = 5 Determine which of the shadow prices will be equal to 0. (c) (5 points) Determine the remaining dual variables by solving the system of linear equations from the dual LP. (d) (5 points) Recheck the obtained solution using the Strong Duality theorem.
For the following linear programming problem: Min -2x + 7y s.t. 5x - 8y ≤ 0 Constraint 1 1x + 1y ≤ 4 Constraint 2 5x - 5y ≤ 3 Constraint 3 -3x + 5y ≤ 6 Constraint 4 1x + 1y ≥ 2 Constraint 5 x, y ≥ 0 a) Solve the LP Model using the graphical method. Provide a graph with all necessary information. State your optimal solution values. b) Find the Slack/Surplus for each constraint. c) Find the Shadow Prices for each constraint.
Dominador T.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD