need help
jsmith2007
linearprograming.docx· 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.
Writeup
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.
QM for Windows or Excel
As previously noted, please set up your problem in QM for Windows or 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.
Click here to view the grading rubric for this assignment.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
COST OF BOOTH - $1,000 PER GAME |
|
|
|
|
|
|
|
|
||
|
LEASE OF A WARMING OVEN - $600 PER 6 GAME SEASON |
|
|
|
|
|
|
||||
|
VENDORS CAN SELL FOOD OR DRINK, BUT NOT BOTH. |
|
|
|
|
|
|
||||
|
PIZZA, HOT DOGS, BARBECUE SANDWICHES WILL BE SOLD. |
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
OVEN HAS 16 SHELVES (36 BY 48 INCHES) = (16*36*48 )* 2 = |
|
55296 |
|
|
|
|
||||
|
FILLS OVEN BEFORE GAME AND BEFORE HALF TIME. |
|
|
|
|
|
|
||||
|
PIZZA DELIVERY COMPANY WILL DELIVER PIZZAS |
|
|
|
|
|
|
||||
|
|
BEFORE GAME AND AFTER KICKOFF. |
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
SALES |
|
SPACE |
|
|
|
|
|
|
|
|
COST |
PRICE |
PROFIT |
REQUIREMENT |
|
|
|
|
|
PIZZA |
[6 / 8] per slice |
0.75 |
1.50 |
0.75 |
24.5 SQUARE INCHES** |
|
|
|
||
|
HOT DOGS |
|
|
0.45 |
1.50 |
1.05 |
16 SQUARE INCHES |
|
|
|
|
|
BARBECUE SANDWICH |
|
0.90 |
2.25 |
1.35 |
25 SQUARE INCHES |
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
INITIAL CASH AVAILABLE - $1,500 |
|
|
|
**COMPUTATION OF PIZZA SLICE SQ. IN. |
|
|||||
|
SALES ESTIMATES |
|
|
|
|
14 INCH SQUARE PIZZA: |
|
|
|
||
|
1 |
PIZZAS >= HOT DOGS + BARBECUE SANDWICHES |
AREA = 14 * 14 = 196 / 8 = |
24.5 |
|
||||||
|
2 |
HOT DOGS >= 2 * BARBECUE SANDWICHES |
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
GOAL: AT LEAST $1,000 PROFIT PER GAME |
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
OBJECTIVE FUNCTION: 3 PRODUCTS WITH PROFITS ABOVE |
|
|
|
|
|
||||
|
|
CONSTRAINTS: |
|
|
|
|
|
|
|
|
|
|
|
1) AVAILABLE MONEY = 1500 |
|
|
|
|
|
|
|
||
|
|
2) OVEN SPACE = 55296 |
|
|
|
|
X1 >= X2 + X3 |
|
|
||
|
|
3) SALES ESTIMATE 1 - ABOVE |
|
|
|
X1 - X2 - X3 >= 0 |
|
|
|||
|
|
4) SALES ESTIMATE 2 - ABOVE |
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
X2 >= 2 * X3 |
|
|
|
|
CALCULATION OF PROFIT PER GAME: |
|
|
|
X2 - 2*X3 >= 0 |
|
|
||||
|
|
OPTIMAL PROFIT FROM LINEAR PROGRAMMING SOLUTION |
|
|
|
|
|
||||
|
|
LESS: COST OF BOOTH PER GAME |
|
|
|
|
|
|
|
||
|
|
LESS: COST OF WARMING OVEN PER GAME |
|
|
|
|
|
|
