Question

(i) You are the cost Engineer for a construction company in charge of building a new

bridge. The construction company will be penalized each day of delay in
construction for bridge. The penalty will be $4500 for the first day and will increase
by $12000 for each following day. Based on its budget, the company can afford to
pay a maximum of $ 155000 toward penalty. By modelling this as an arithmetic
progression, find the maximum number of days by which the completion of work can
be delayed. ​

Answer 1

approximately 13 days

Explanation:

Answer 2

The work can only be delayed for 13 days

Explanation:

The construction company will be penalized $4500 for delaying the project for the first day after that day the amount will increase by $12000 for each day. The company can only afford to pay $155000 towards the penalty.

Using arithmetic progression,

a = 4500

d = common difference = 12000

nth term = 155000

n = number of days

a + (n - 1)d = 155000

4500 + (n - 1)12000 = 155000

4500 + 12000n - 12000 = 155000

12000n - 7500 = 155000

12000n = 162500

divide both side by 12000

n = 162500/12000

n = 13.5416666667

n = 13.5

The work can only be delayed for 13 days