Mathematical Techniques in Construction: Tasks and Scenarios

You are employed by a large design and build contractor , as a design build technician. Your supervisor has
recognised that this mathematical unit would benefit and support you both in terms of completing your Higher
National studies but also in understanding how mathematical techniques could be applied to varying construction situations.

Your supervisor also reconises that some advanced mathematical techniques will be needed in future studies and therefore has developed a series of tasks to support you in the understanding of techniques included within tasks are advanced , it is hoped that all tasks will be attempted. 

You have been contracted as a mathematical consultant to solve and confirm a number of mathematical
problems/solutions for projects on a major contract.

1. A building services engineer is to design a water tank for a project. The tank has a rectangular area of 26.5m2. With the design specifics of the width being 3.2m shorter than the length, calculate the length and width to 3 significant figures for resourcerequirements.

 

2. As an employee of company JR construction you have received a letter regarding the project your company is working on. It has a penalty clause that states the contactor will forfeit a certain some of money each day for late completion. (i.e. the contractor gets paid the value of the original contract less any sum forfeit). If she is 5 days late she receives £4250 and if she is 12 days late she receives £2120. Calculate the daily forfeit and determine the original contract.

A) In the new Epiphyte Engineering factory 5000 light bulbs Type A are installed. Their lengths of life are normally distributed with a mean of 360 days and a standard deviation of 60 days.

a) If it is decided to replace all bulbs at one specified time, what interval must be allowed between replacements if not more than 10% of bulbs should fail beforereplacement?
b) What practical considerations might dictate such a replacement policy?
c) The supplier offers a new type of bulb, Type B, that has a mean life of 450 days and the same standard deviation (60 days) as the present type. If these bulbs were to be used how wouldthe replacement time be affected?
d) Determine whether the new type of bulb is preferable given that is costs 25% more thanthe HNC/HND Construction and the Built Environment 7 existing Type A. Present and explain your conclusions.
f) A rival supplier now offers a third type of bulb, Type C, that has a mean life of 432 days and a standard deviation of 45 days. If these bulbs were to be used how would the replacement timebe affected?
How should the Type C bulb compare for costs if it is to be adopted? Present and explain your conclusion.

 

(B) A simple random sample of 10 people from a certain population has a mean age of 27 years. Can we conclude that the mean age of the population is not 30 years? The variance of the populate ages is known to be 20. Test your chosen hypothesis at a 5% level of significance using both a two tailed test and a one tailed test and explain your conclusions.