all of problem 2 and 3

Problem 1 Body Mass Index (BMI) is a measure for adults to use to see if they are a healthy weight for their height. Use the calculation given here [url removed, login to view] For people with weights between 40kg and 170kg and heights between 148cm and 200cm, write a Maple procedure to input a weight and height and output the corresponding BMI value and its weight status in an appropriate statement. If the BMI is within 1 BMI unit of an interval’s boundary, a statement should be added indicating that the BMI is borderline. BMI Weight Status Below 18.5 underweight 18-5 – 24.9 normal 25.0 – 29.9 overweight 30.0 + obese MA4001: Logic and Problem Solving 2014-15 GROUP COURSEWORK Page 2 of 3 Your tests of your procedure should include the following values, which should be included in your final presentation ... Weight Height 53 [url removed, login to view] 55 [url removed, login to view] 72.5 [url removed, login to view] 77.5 [url removed, login to view] 101 [url removed, login to view] 93 [url removed, login to view] 38 1.7 -6 1.5 (25%) Problem 2 Read the description of the problem and then answer the questions that follow. You are a business adviser providing expert advice on request. Your client is a snack stall, Daily Snacks, which can sell whatever it can produce. A requirement of the stall location is it must serve at least 100 customers each day. Snacks take 1 minute each to produce and sell for 20 pence. Each Soup takes 2.5 minutes to produce and sells for 30 pence. Daily Snacks’ objective is to maximise the total revenue for the stall, given that it has 200 preparation minutes available each day and at least 40 soups must be served. Questions You should answer the following questions and incorporate your answers into a wordprocessed report to form part of your final pdf. 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. (6%) 2. Solve the problem graphically (use graph paper). (8%) 3. Solve the problem using the Excel Solver and interpret the results. (8%) 4. Find the value of the slack-variable relating to the minutes available and discuss its economics interpretation. (5%) 5. Find the shadow price of minutes available and discuss its economic interpretation. (5%) 6. Suppose Daily Snacks can produce no more than 75 snacks each day. What should be the combination of snacks and soups now? (12%) MA4001: Logic and Problem Solving 2014-15 GROUP COURSEWORK Page 3 of 3 7. For the final part of your report, in your capacity as an 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 baking and delivering, but who knows nothing about the subject of linear programming. You may use tables and charts if you wish. (6%) 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
= 60 −  , 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. (5%) 2. By plotting the revenue and cost functions found in Q1 above obtain the break even output levels and corresponding price. (10%) 3. Calculate the profit-maximising level of output and the profit at this output level. (5%) Presentation of the documentation (5%)