(A) Using slack variables, determine the initial system for the linearprogramming problem.(B) Write the simplex tableau and identify the first pivot and theentering and exiting variables.(C) Use the simplex method to solve the problem.First constraintSecond constraintObjective function***X₁, X2, S1, S₂ 20Maximizesubject to(A) Using slack variables, determine the initial system for the linear programming problem. Use s, for the firstconstraint and s₂ for the second constraint.P= 16x₁ + x24x₁ + x₂ ≤20X₁ + 8x₂ ≤20X₁, X₂ 20

Given linear programming problem is: Maximize P=16x1+x2subject to4x1+x2≤20x1+8x2≤20x1, x2≥0 To Do:…

Answered: (A) Using slack variables, determine…

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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Formulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 4 labor-hours. In a certain week, the company has 2800 board feet of wood available and 560 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize P = subject to the constraints board feet labor-hours x ≥ 0 y ≥ 0
Snack A provides 10 grams of protein and costs 2 dollars, snack B provides 6 grams of protein and costs 3 dollars. You need at least 30 grams of protein a day. Let x be the number of snack A you buy and y be the number of snack B you buy. You want to minimize cost. State the linear programming problem in mathematical terms, identifying the objective function and constraints. Do not solve the problem to completion. Just state the inequalities needed and the objective function.
(A) Using slack variables, determine the initial system for the linear programming problem. (B) Write the simplex tableau and identify the first pivot and the entering and exiting variables. (C) Use the simplex method to solve the problem. P = 16x, + 12x2 2x1 + X2 58 X1 + 8x2 58 X1, X2 2 0 Maximize subject to
Write the transportation problem as a linear programming problem in terms and solvent of x and y and solve. (Indicate the number of units that should be transported from each factory to each depot and the total transportation cost.)
Formulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 5 labor-hours. In a certain week, the company has 2800 board feet of wood available and 500 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize P = subject to the constraints board feet labor-hours x ≥ 0 y ≥ 0
Formulate a linear programming problem that can be used to solve the following question. An individual needs a daily supplement of at least 380 units of vitamin C and 64 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 34 units of vitamin C and 4 units of vitamin E, while each ounce of food II contains 20 units of vitamin C and also 12 units of vitamin E. The total supplement of these two foods must be at most 29 ounces. Unfortunately, food I contains 22 units of cholesterol per ounce and food II contains 32 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. X = ---Select--- y = --Select--- ---Select--- | F = Subject to (objective function) (total ounces of food) (units of vitamin C) (units of vitamin E) x ---Select--- 0, y ---Select--- 0 (nonnegativity constraint)
Formulate a linear programming problem that can be used to solve the following question. A dealer has 8900 pounds of peanuts, 6000 pounds of almonds, and 3800 pounds of cashews to be used to make two mixtures. The first mixture wholesales for $2.40 per pound and consists of 60% peanuts, 30% almonds, and 10% cashews. The second mixture wholesales for $3.20 per pound and consists of 15% peanuts, 45% almonds, and 40% cashews. How many pounds of each mixture should the dealer make to maximize revenue? x = ---Select--- y = ---Select--- ---Select--- v|F= Subject to (objective function) (pounds of peanuts) (pounds of almonds) (pounds of cashews) x ---Select--- 0, y ---Select--- 0 (nonnegativity constraint)
A farmer wishes to buy some goats and cows. He has pasture for only 50 animals. Goats cost $300 each and cows $600 each. He can expect to make a profit of $250 on each goat and $350 on each cow. If he has $24000 to spend and he buys g goats and c cows, I. Formulate a linear programming model for this situation. II. Using a graph, find the numbers of goats and cows that will maximize profit. III. State the maximum profit.

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