Logic and Problem Solving
Project description
Problem 1
Salary Taxed at
First £2,710 0%
£2,711 – £34,370 20%
£34,371 + 40%
Write a Maple procedure, tax, to calculate (to the nearest pound) the tax a person owes, depending on his/her salary.
Calculate the tax using this table:
The procedure should show
i) the salary,
ii) the tax rate,
iii) the amount of tax
iv) the amount left after tax
v) and be able to deal with any input, valid or not
and
vI) Your submission must include output from the following test data
tax(2000)
tax(2810)
tax(34371)
tax(34471)
(25%)
Problem 2
Read the description of the problem and then answer the questions that follow.
You are an Independent IT Adviser providing expert advice to individuals on request. A client of a small newspaper, Daily News, produces two editions, morning and evening, and must publish at least 100 total copies for each day’s delivery. The morning edition requires 1 hour of preparation and sells for 20 pence. The evening edition requires 2.5 hours of preparation and sells for 30 pence. The client’s objective is to maximise his total revenue of publishing, given that he has 200 preparation hours available each day and at least 40 copies of the evening edition must be printed each day.
Questions
You should answer the following questions and incorporate your answers into a word-processed report. The sections of your report should correspond to the individual questions following.
1. Formulate the client’s problem as a linear programming model, clearly defining the variables, the objective function and the constraints.

2. Solve the problem graphically (use a graph paper).

3. Solve the problem using the Excel Solver and interpret the results.

4. Find the value of the slack-variable relating to the hours available and discuss its economics interpretation.

5. Find the shadow price of hours available and discuss its economics interpretation.

6. Suppose that the Daily News can produce no more than 75 copies of the morning edition each day. What should be the newspaper mix?

7. For the final part of your report, in your capacity as an IT Adviser, you should present a memorandum to your client. Describe your main conclusions in simple, non-technical English; i.e. do not use technical terms like variable, objective function or dual price. Don’t worry about repeating some or all of the points that you have already made in answer to earlier questions. The aim is to communicate your conclusions clearly to someone who is knowledgeable about newspaper production, but who knows nothing about the subject of linear programming. You may use tables and charts if you wish.

Problem 3
A company manufactures a product. The total fixed costs are £400 and the variable cost per unit is £10. The total revenue function is given by R= (60 – q) q, where q is the quantity sold.
Questions
You should answer the following questions and incorporate your answers into a word-processed report. The sections of your report should correspond to the individual questions below.
1. Find an expression for total costs in terms of q, the quantity produced.

2. By plotting the revenue and cost functions found in 1 above obtain the break even output levels and corresponding price.

3. Calculate the profit-maximising level of output and the profit at this output level.

4. Presentation of the documentation