MAT 540 Week 8 Assignment 1 Toys R’ Us sells two types of toys

Toys R’ Us sells two types of toys, Barbie house (toy A) and Dizzie’s condo (toy B). The store owner pays $8 and $14 for each one unit of toy A and B respectively. One unit of toys A yields a profit of $2 while a unit of toys B yields a profit of $3. The store owner estimates that no more than 2000 toys will be sold every month and he does not plan to invest more than $20,000 in inventory of these toys. How many units of each type of toys should be stocked in order to maximize his monthly total profit?

Answer the following:Toy AToy B

1.       What is the objective function?Objective function$0.00 $0.00 

2.       Is this a minimization or maximization problem? Constraint Used Available Left over

3.       Identify the constraints? Units assembled 1 1 <= 0 0 0

4.       Is this a non-negativity constraint model? Cost per unit $0.00  $0.00  <= $0.00   $-    $0.00 

5.       Graph the problem and identify the regions that hold the feasible region. You can do this by hand or use excel or POM-QM.

6.       What are the vertices of the scenario?Decision Variables

7.       What is the most optimal solution?Toy A0

8.       What is the optimal value?Toy B0

9.       Provide all resources used when computing this work. Include all drawings and sketches if any, by hand.Objective function

$0.00

 

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.

Excel.

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.