Linear Programming

Problem 1

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 80 customers each day.

Snacks take 1 minute each to produce and sell for 30 pence. Each Soup takes 2.5 minutes to produce and sells for 45 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 32 soups must be served.

Questions

You should answer the following questions and incorporate your answers into a word-processed 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. 4 Constraints

(6%)

2. Solve the problem graphically (use graph paper). Must show results

(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 60 snacks each day. What should be the combination of snacks and soups now?

(12%)

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.

Programación lineal Matemáticas

Nº del proyecto: #15007523

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