1. (12pts.) A) Find the dual linear program to the primal linear program. Hint: you should rewrite constraints so that they fit one of the forms discussed. minimize 3x1 + 2x2 subject to x1 + x2 ? 3 0 ? x1 ? 3 x2 ? 0. B) Given the dual linear program, find the primal linear program maximize y1 + 3y2 + 4y3 subject to 3y1 + 5y2 + 2y3 ? 1 2y1 + y2 + 5y3 ? -5 y1 + y2 + y3 ? -1 y2 ? 1 y3 ? -2
Added by F-Tima N.
Close
Step 1
Rewrite the primal linear program in standard form: minimize \(3x_1 + 2x_2\) subject to \(-x_1 - x_2 \leq -3\) \(x_1 \leq 3\) \(x_2 \geq 0\) Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 80 other Calculus 3 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
State the dual problem for each linear programming problem. Minimize $$w=y_{1}+y_{2}+4 y_{3}$$ subject to: $$\begin{aligned} y_{1}+2 y_{2}+3 y_{3} & \geq 115 \\ 2 y_{1}+y_{2}+8 y_{3} & \geq 200 \\ y_{1} &+y_{3} \geq 50 \end{aligned}$$ with $$y_{1} \geq 0, \quad y_{2} \geq 0, \quad y_{3} \geq 0$$
Linear Programming:The Simplex Method
Minimization Problems; Duality
State the dual problem for each linear programming problem. Maximize $$z=2 x_{1}+7 x_{2}+4 x_{3}$$ subject to: $$\begin{aligned} 4 x_{1}+2 x_{2}+x_{3} & \leq 26 \\ x_{1}+7 x_{2}+8 x_{3} & \leq 33 \end{aligned}$$ with $$x_{1} \geq 0, \quad x_{2} \geq 0, \quad x_{3} \geq 0$$
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD