Consider the following statements.(i) The feasibility set of a linear programming problem always contains the origin.(ii) The solution of a linear programming problem can occur at a point which is not an extreme point of thefeasibility set.(iii) Every linear programming problem with a non-empty, bounded feasibility set has a solution.(iv) Slack variables are introduced in order to change the sign of inequalities in a linear programmingproblem.Determine which of the above statements are True (1) or False (2).

(i) True. The feasibility set of a linear programming problem is the set of all feasible solutions,…

Answered: Consider the following statements. (i)…

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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Determine whether the following statement is true or false, and explain why. A surplus variable of a linear programming problem can never have a negative value during the intermediate steps of the simplex method. Choose the correct answer below. O A. The statement is true. A surplus variable always has a positive value during every step of the simplex method, including intermediate steps. B. The statement is false. A surplus variable cannot have a negative value at the beginning or end of the simplex method. It almost always has a negative value during at least some of the intermediate steps. C. The statement is true. A surplus variable can never have a negative value during any step of the simplex method, including intermediate steps. D. The statement is false. A surplus variable cannot have a negative value at the beginning or end of the simplex method. It may have a negative value during an intermediate step.
Identify if the given linear programming problem is a standard maximization problem. If it is a standard maximization problem, then express the constraints as slack variable equations, write the objective function in standard form, and set up the initial simplex tableau. If it is not a standard maximization problem, then explain all the reasons why it is not and type NA (or Not Applicable) in the remaining boxes. Maximize: P=100x+200y+50z subject to: 5x+5y+10z≤1000 10x+5y≤50 0≤x, 0≤y, 0≤z Standard Max Answer Here, Yes or No with reasons (Keyboard only): Slack Variable Equations Here: (enter NA if it is not a standard maximization problem) Objective Function in Standard Form Here: (enter NA if it is not a standard maximization problem) Initial Simplex Tableau Here: (enter NA if it is not a standard maximization problem)
Formulate but do not solve the following exercise as a linear programming problem. A financier plans to invest up to $400,000 in two projects. Project A yields a return of 10% on the investment of x dollars, whereas Project B yields a return of 13% on the investment of y dollars. Because the investment in Project B is riskier than the investment in Project A, the financier has decided that the investment in Project B should not exceed 40% of the total investment. How much should she invest in each project to maximize the return on her investment P in dollars? MaximizeP= subject to the constraints ? amount available for investment? allocation of funds?
(a) u want to send these shipments as cheaply as possible. Formulate this as a linear program ( do not need to formulate it is standard inequality form) (b) all is the same as (a) but that only 220L of important chemical A are now required at warehouse 1 or 2 for storage, the company must pay transportation costs or can be disposed of at the port in which case the company paus no transportation costs but pays a disposal fee of £16 per L. You want to find how to ship or dispose of all 610L of chemical imported at the mimimum cost while still ensuring that required amounts (220L and 330L respectively) delivered to warehouse 1 and 2. Describe how to modify your linear program from previous question.
Determine whether the following linear programming problem is infeasible, unbounded, or has multiple optimal solutions. Draw a graph and explain your conclusion. Maximize 400x + 500y Subject to 2x + 1y > 60 -3x + 4y < 90 x, y > 0
(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
Formulate but do not solve the following exercise as a linear programming problem.A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $3 on each unit of Product A and $5 on each unit of Product B. To manufacture a unit of Product A requires 5 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 5 min on Machine II. There are 269 min available on Machine I and 205 min available on Machine II in each work shift. How many units of a product should be produced in each shift to maximize the company's profit P in dollars? Maximize P = subject to the constraints Machine I Machine II x ≥ 0 y ≥ 0
1. Set up a linear programming model of the situation described. Determine whether it is in standard form. If not make it standard. A restaurant chef is planning a meal consisting of two foods, A, and B. • Each kg of A contains 3 units of fat and 6 units of protein • Each kg of B contains 1 unit of fat and 3 units of protein The chef wants the meal to consist of at least 18 units of protein and at most 6 units of fat. If the profit that he makes is 3 dollars per kg for food A and 5 dollars for food B, how many kilograms of each food should be served so as to maximize his profit?
Plz expert don't Use chat gpt Solve completely
Formulate but do not solve the following exercise as a linear programming problem.TMA manufactures 37-in. high-definition LCD televisions in two separate locations: Location I and Location II. The output at Location I is at most 6500 televisions/month, whereas the output at Location II is at most 5300 televisions/month. TMA is the main supplier of televisions to Pulsar Corporation, its holding company, which has priority in having all its requirements met. In a certain month, Pulsar placed orders for 3000 and 3600 televisions to be shipped to two of its factories located in City A and City B, respectively. The shipping costs (in dollars) per television from the two TMA plants to the two Pulsar factories are as follows. To Pulsar Factories From TMA City A City B Location I $6 $4 Location II $8 $7 TMA will ship x televisions from Location I to City A and y televisions from Location I to City B. Find a shipping schedule that meets the requirements of both…

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