**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 wonâ€™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 parag__raph 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

Q7 | Grade | Scale | Probability | Expected Value | Variance | ||||||||

A | 4 | 0.1 | |||||||||||

B | 3 | 0.2 | |||||||||||

C | 2 | 0.4 | |||||||||||

D | 1 | 0.2 | |||||||||||

F | 0 | 0.1 | |||||||||||

1 | Expected Grade | ||||||||||||

Course Variance | |||||||||||||

Q8 | Economic Conditions | ||||||||||||

Investment | Good | Poor | |||||||||||

Probability | 0.45 | 0.55 | A: | ||||||||||

A | $380,000 | ($100,000) | B: | ||||||||||

B | 130,000 | 85,000 | Choose investment A or B? | ||||||||||

Q9 | Distribution | Mean | Standard deviation | Lower weight limit | Upper weight Limit | Probability | Upper limit | ||||||

Normal | 45 | 5 | 38 | 50 | Lower Limit | ||||||||

Probability | (in between upper and lower limits) | ||||||||||||

Note: probability from the upper limit to -infinity is 0.7734 | |||||||||||||

Q10 | Distribution | Mean | Standard deviation | Occupied | Probability NOT occupied | ||||||||

Normal | 15 | 5 | 18 | Occupuied | |||||||||

Not occupied | |||||||||||||

Q11 | Distribution | Mean | Standard deviation | Probability | Number of recorders ordered | ||||||||

Normal | 175 | 55 | 0.85 | ||||||||||