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Answer questions 7 to 8 according to the feasible region given in the graph on the right. 7) Which of the following points is the optimal solution for the objective function: MAX z = 20 x₁+ 10 x₂? 8) Which of the following points is the optimal solution for the objective function: MIN z = 5 x₁+ 10 x₂?

Answer questions 7 to 8 according to the feasible region given in the graph on the right. 7) Which of the following points is the optimal solution for the objective function: MAX z = 20 x₁+ 10 x₂? 8) Which of the following points is the optimal solution for the objective function: MIN z = 5 x₁+ 10 x₂?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A company wants to produce bowls and mugs and plans to sell them at a profit of $10 per bowl and $15 per mug. Each bowl costs $5 dollars to produce and each mug costs $4 to produce. The company has a budget of $2000 for production. It also has shelf space that holds 500 bowls, and a bowl takes twice as much space as a mug. Assuming that your decision variables x₁ and x₂ represent the number of bowls and mugs to be produced, respectively, answer the questions 1 to 3 accordingly: 1) Which of the following is the correct objective function for this problem? 2) Which of the following is the correct budget constraint? 3) Which of the following is the correct space constraint? Answer questions 4 to 6 according to the feasible region for the following constraints using the graph and the bold points on the right: X₁+2 X₂ 24 3 x₁ + x₂ 56 X₁ ≥ 0, X₂20 4) How many of the bold points are feasible? 5) How many of the bold points are infeasible? 6) Given any objective function, how many of the bold points have the potential to be an optimal solution? Answer questions 7 to 8 according to the feasible region given in the graph on the right. 7) Which of the following points is the optimal solution for the objective function: MAX z = 20 x₁+ 10 x₂? 8) Which of the following points is the optimal solution for the objective function: MIN z = 5 x₁+ 10 x₂? Assuming that x, and x₂ are nonnegative, answer questions 9 to 10 with the help of the graph on the right. 9) Which of the following linear programs has an unbounded solution? MIN Z=X₁ + X₂ s.t. x₁ ≤ 2 X₂ 52 MAX Z= X₁ + X₂ s.t. x₁ ≤ 2 X₂ 22 MAX Z= X₁ + X₂ s.t. X₁ ≤ 2 X₂ ≤ 2 MIN Z X₁ + X₂ s.t. x₁ 2 2 X₂ ≤ 2 MIN Z=X₁ + X₂ s.t. x₁ $2 X₂ 22 MIN Z=X₁ + X₂ s.t. x₁ 2 2 X₂ 22 6 3 N X₂ 1+ D 5 X₁ +
Transcribed Image Text:A company wants to produce bowls and mugs and plans to sell them at a profit of $10 per bowl and $15 per mug. Each bowl costs $5 dollars to produce and each mug costs $4 to produce. The company has a budget of $2000 for production. It also has shelf space that holds 500 bowls, and a bowl takes twice as much space as a mug. Assuming that your decision variables x₁ and x₂ represent the number of bowls and mugs to be produced, respectively, answer the questions 1 to 3 accordingly: 1) Which of the following is the correct objective function for this problem? 2) Which of the following is the correct budget constraint? 3) Which of the following is the correct space constraint? Answer questions 4 to 6 according to the feasible region for the following constraints using the graph and the bold points on the right: X₁+2 X₂ 24 3 x₁ + x₂ 56 X₁ ≥ 0, X₂20 4) How many of the bold points are feasible? 5) How many of the bold points are infeasible? 6) Given any objective function, how many of the bold points have the potential to be an optimal solution? Answer questions 7 to 8 according to the feasible region given in the graph on the right. 7) Which of the following points is the optimal solution for the objective function: MAX z = 20 x₁+ 10 x₂? 8) Which of the following points is the optimal solution for the objective function: MIN z = 5 x₁+ 10 x₂? Assuming that x, and x₂ are nonnegative, answer questions 9 to 10 with the help of the graph on the right. 9) Which of the following linear programs has an unbounded solution? MIN Z=X₁ + X₂ s.t. x₁ ≤ 2 X₂ 52 MAX Z= X₁ + X₂ s.t. x₁ ≤ 2 X₂ 22 MAX Z= X₁ + X₂ s.t. X₁ ≤ 2 X₂ ≤ 2 MIN Z X₁ + X₂ s.t. x₁ 2 2 X₂ ≤ 2 MIN Z=X₁ + X₂ s.t. x₁ $2 X₂ 22 MIN Z=X₁ + X₂ s.t. x₁ 2 2 X₂ 22 6 3 N X₂ 1+ D 5 X₁ +
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