4) Max Z = 4x1 + 8x2s.t.2x1 + 4x2 ≤ 146x1 + 2x2 ≤ 12Xi ≥ 0Problem 4 should be graphed first. Consider where the objective function is intersecting with the feasibleregion. How will this affect the solution (which point is optimal)? How would you describe this problemin real production terms?

Given data is Max Z=4x1+8x2 Subject to constraints: 1.) 2x1+4x2≤142.) 6x1+2x2≤12xi≥0

Answered: 4) Max Z = 4x1 + 8x2 s.t. 2x1 + 4x2 <…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 53P

See similar textbooks

Similar questions

This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.
Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company experts to estimate product demand. Then we use Excels trend curve fitting capabilities to fit a quadratic function that represents that segments demand function. Finally, we add the segment demand curves to derive an aggregate demand curve. Try this procedure for pricing a candy bar. Assume the candy bar costs 0.55 to produce. The company plans to charge between 1.10 and 1.50 for this candy bar. Its marketing department estimates the demands shown in the file P07_47.xlsx (in thousands) in the three regions of the country where the candy bar will be sold. What is the profit-maximizing price, assuming that the same price will be charged in all three regions?
Consider the following LP problem with two constraints: 18X + 8Y >= 144and 9X + 4Y= 36. The objective function is Min 14X + 30Y . What combination of X and Y will yield the optimum solution for this problem? a. infeasible problem b. unbounded problem c. 0 , 9 d. 4 , 0 e. 2 , 4.5
Find the optimal solution for the following problem. Maximize C = 4x + 12y subject to 3x + 5y ≤ 12 6x + 2y ≤ 10 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y? (Round your answer to 3 decimal places.) What is the maximum value of the objective function? (Round your answer to 3 decimal places.)
4. Consider the following linear programming problem: Maximize Z=$15x + $5y, subject to (1) 2x + y ≤ 10 and (2) 4x + 3y ≤ 24 and (3) x, y ≥ 0. Will the optimal solution change if the objective function becomes Maximize Z=$15x + $20y (constraints remain the same)? Select one: a. Can't determine given the information. b. Yes, it will change. c. No, it remains the same.
Consider the following LP model in standard form, with a row for the objective function Z. a) Put it into Canonical form ( or Simplex Tableau form) with basic variables X1, X2 , and X3. b) Determine the association BFS (Basic Feasible Solution) and the new formula for the objective function Z Minimize 10X1 + 4X2 Sujbject to 3X1 + 2X2 - X3 = 60 7X1 + 2X2 - X4 = 84 3X1 + 6X2 -X5 = 72 X1, X2, X3 , X4 , X5 >= 0
Consider the following set of constraints: -4X <= -512; -28Y <= -3584; 0.5 X + 14Y >= 1792, and 2X + 2Y <= 256. Pick a right statement for this problem: a. Feasible region is represented by a line and multiple feasible points are available. b. The feasible region is defined by a single (unique) point. c. Feasible region does not exist. d. All the options are incorrect. e. Solution to this problem cannot be found without the objective function
Given this linear programming model, solve the model and then answer the questions that follow.Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc.Subject toMachine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hoursMaterials 2x1 + 2x2 + 4x3 ≤ 200 poundsProduct 2 x2 ≤ 16 units x1, x2, x3 ≥ 0 a. Are any constraints binding? If so, which one(s)?
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= 3x+7y subject to: 2x-6y≤9 x+5y≤-14 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)
1. Compare the LP relaxations of the three integer optimization problems: (Problem 1) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. 28*x1 + 15*x2 + 13*x3 + 12*x4 <= 39x1, x2, x3, x4 \in {0,1} (Problem 2) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. 2*x1 + x2 + x3 + x4 <= 2x1, x2, x3, x4 \in {0,1} (Problem 3) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. x2 + x3 + x4 <= 2x1 + x2 <= 1x1 + x3 <= 1x1 + x4 <= 1x1, x2, x3, x4 \in {0,1} Among these three problems, the LP relaxation of which problem can offer a solution whose objective value is closer to the optimal value of the corresponding integer optimization? Problem 2 Problem 3 Problem 1
Canine LLC makes two types of dog food: Formula S and Formula X. They use linear programming model to determine the optimum mix of dog food to produce. The model they use is given below: Maximize: 50S + 60X Subject to these constraints: 8S + 10X ≤ 800 S + X ≤ 120 4S + 5X ≤ 500 S, D ≥ 0 Based on the information given above, the maximum value of the confectioner's linear programming is $_______.
use the simplex method to solve the given linear programming problem (In each case the objective function is to be maximized.) Objective function: z = x_{1} - x_{2} + 2x_{3} Constraints: 2x_{1} + 2x_{2} <= 8 x_{3} <= 5 x_{1}, x_{2}, x_{3} >= 0

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

SEE MORE TEXTBOOKS