## Quantitative Assignment

**A furniture company manufactures desks and chairs. Each desk uses four units of wood, and each chair uses three units of wood. A desk contributes $250 to profit, and a chair contributes $145. Marketing restrictions require that the number of chairs produced be at least four times the number of desks produced. There are 2000 units of wood available.****Use Solver to maximize the company’s profit.Confirm graphically that the solution in part****a maximizes the company’s profit.Use SolverTable to see what happens to the decision variables and the total profit when the availability of wood varies from 1000 to 3000 in 100-unit increments. Based on your findings, how much would the company be willing to pay for each extra unit of wood over its current 2000 units?**How much profit would the company lose if it lost any of its current 2000 units?

2-There are three factories on the Momiss River. Each emits two types of pollutants, labeled *P*1 and *P*2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1500 to process a ton of factory 1 waste, and each ton processed reduces the amount of *P*1 by 0.10 ton and the amount of *P*2 by 0.45 ton. It costs $2500 to process a ton of factory 2 waste, and each ton processed reduces the amount of *P*1 by 0.20 ton and the amount of *P*2 by 0.25 ton. It costs $3000 to process a ton of factory 3 waste, and each ton processed reduces the amount of *P*1 by 0.40 ton and the amount of *P*2 by 0.50 ton. The state wants to reduce the amount of *P*1 in the river by at least 125 tons and the amount of *P*2 by at least 175 tons.

**a)Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Are the LP assumptions (proportionality, additivity, divisibility) reasonable in this problem?**

**b)Use SolverTable to investigate the effects of increases in the minimal reductions required by the state. Specifically, see what happens to the amounts of waste processed at the three factories and the total cost if both requirements (currently 125 and 175 tons, respectively) are increased****by the** **same****percentage. Revise your model so that you can use SolverTable to investigate these changes when the percentage increase varies from 10% to 100% in increments of 10%. Do the amounts processed at the three factories and the total cost change in a linear manner?**

**Submit:**Please submit your work as one Excel file. (You should have multiple worksheets in the file, each of which is labeled with the problem number). Select this template to access the Excel workbook for these problems. Alternative template for Mac users.

There are two spreadsheet problems in Module 2. Be sure to complete each one. Include appropriate variable color coding and use Range Names Understanding the use and value of range names is very important, especially with more complex models. Here are a few comments regarding the Module 2 problems:

**1- Manufacturing Desks and Chairs**

Be sure to complete all parts (A, B, C) of the problem. Part B asks you to confirm the solution graphically. This is a simple graphic used to illustrate the optimal solution (125 tables, 500 chairs) given 2000 units of wood available (constraint) and a 1:4 market constraint (tables:chairs). A simple xy axis graphic is acceptable. Part C is using Solver Table. Note: if your model is not set-up correctly, Solver Table will not give you the correct results. So….don’t always blame S-T if you have a problem.

**2- River Pollutants**

There are two parts (A, B) to this spreadsheet problem. However, part A has two questions. Respond to both questions. The “LP Assumptions” question can get overlooked.

Carefully populate your spreadsheet with the INPUT data from the text. For Part B, you will have to add some addition math functions to your basic model to enable Solver Table to do its analysis (scaling of the “Required” values. The “Required” values (125,175) need to be increased in a range of 10% to 100%, in increments of 10%.

These are not difficult problems, so don’t over-think what is required. Go step by step. Identify your INPUTs – post them and color code blue. Identify the Objective/ Result – color code gray. Identify your decision variables – color code (Light) red — leave cell blank unless asked to populate these cells. Solver will do it for you. Then, determine formulas required for enabling the analysis process by Solver.