MAT-540 WeeK 8 Assignment 1
You are to solve Problem 30 in Chapter 4 on page 158 of your textbook. It’s about publishing three weekly magazines. You can use QM for Windows to perform a sensitivity analysis for Objective function coefficients and the RHS values of the constraints. Be sure give the shadow price/dual values for an extra hr of production time or an extra lb of paper.
Be sure to follow instructions written for Assignment 1, Linear Programming Case Study.
Assignment 1. Linear Programming Case Study
Your instructor will assign a linear programming
project for this assignment according to the following specifications.
It will be a problem with at least three (3) constraints and at least two (2) decision variables. The problem will be bounded and feasible. It will also have a single optimum solution (in other words, it won’t have alternate optimal solutions). The problem will also include a component that involves sensitivity analysis and the use of the shadow price.
You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet showing your work.
Your writeup should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one (1) or two (2) succinct paragraphs.
After the introductory paragraph, write out the L.P. model for the problem. Include the objective function and all constraints, including any non-negativity constraints. Then, you should present the optimal solution, based on your work in Excel. Explain what the results mean.
Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.
As previously noted, please set up your problem in Excel and find the solution using Solver. Clearly label the cells in your spreadsheet. You will turn in the entire spreadsheet, showing the setup of the model, and the results.
A publishing house publishes three weekly magazines—Daily Life, Agriculture Today, and Surf ’s Up. Publication of one issue of each of the magazines requires the following amounts of production time and paper:
Production (hr.) Paper (lb.)
Daily Life 0.01 0.2
Agriculture Today 0.03 0.5
Surf’s Up 0.02 0.3
Each week the publisher has available 120 hours of production time and 3,000 pounds of paper. Total circulation for all three magazines must exceed 5,000 issues per week if the company is to keep its advertisers. The selling price per issue is $2.25 for Daily Life, $4.00 for Agriculture Today, and $1.50 for Surf’s Up. Based on past sales, the publisher knows that the maximum weekly demand for Daily Life is 3,000 issues; for Agriculture Today, 2,000 issues; and for Surf’s Up, 6,000 issues. The production manager wants to know the number of issues of each magazine to produce weekly in order to maximize total sales revenue.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.