Suppose that you have been asked to take over as a project manager on a small construction project which has been decomposed into 7 tasks – activities. Let Qi be the quantity of work for task i (expressed in labor days/machine days/ days needed to process the total amount of material per task), Li be the no. of labor required per task i, Mi be the amount of material required for task i, Ei be the no. of the construction equipment required for task i, Ti be the duration of task i in days. The given quantity of work is as follows:

Qi (for Mi) =12 in Task 1
Qi (for Li )= 20 in Task 2
Qi (for Ei) = 14 in Task 3
Qi (for Li) = 10 in Task 4
Qi (for Ei) = 9 in Task 5
Qi (for Mi ) = 12 in Task 6
Qi(for Ei) = 6 in Task 7

Task Li Ei Mi Ti
1 2 0 3
2 2 5 5
3 3 6 7
4 3 7 5
5 2 4 3
6 1 3 2
7 1 4 2

a) Determine manpower for tasks 2 and 4, materials for task 1 and 6, equipment requirements for tasks 3, 5 and 7 of a given construction situation. Calculate the total labor power and project duration.
b) Assume that the wage rate is £15/hr .Calculate the manpower cost for the initial project. If the project has to be completed in 20 days, you have to make a decision on increasing/decreasing a labor power. What is the suggested labor power in that case? Compare and contrast your solution to construction situation in terms of the total labor cost required for the initial project.
c) If an initial account of £47500 is invested for material payments in a construction project with 5% additional costs per day, how long should the project last before it triples its expenses?
d) Use the data on the no. of workers required (Li) and the quantity of work for task i (Qi) in order to prepare the appropriate graph. Fit straight line to the data using least squares method. Using the equation of the line of the best fit, estimate the value of Qi if Li is 5. What would be the duration (in days) of the task in that case?
e) Effective judgments have been made in relation to the choice of the total labor cost required for the project in Question b).
f) Check the validity of your estimated law in Question d) using the Pearson Correlation Coefficient.
g) Comment critically on how good you expect the forecast of Qi calculated in
Question d) to be.

a) To determine the manpower for tasks 2 and 4, materials for task 1 and 6, and equipment requirements for tasks 3, 5, and 7, we need to refer to the given quantities of work (Qi), labor required (Li), amount of material required (Mi), equipment required (Ei), and duration (Ti) for each task.

For task 2:
Manpower (Li) = 2
Materials (Mi) = 5

For task 4:
Manpower (Li) = 3

For task 1:
Materials (Mi) = 12

For task 6:
Materials (Mi) = 12

For task 3:
Equipment (Ei) = 14

For task 5:
Equipment (Ei) = 9

For task 7:
Equipment (Ei) = 6

To calculate the total labor power, we sum up the manpower required for all tasks:
Total Labor Power = Li (for task 1) + Li (for task 2) + Li (for task 3) + Li (for task 4) + Li (for task 5) + Li (for task 6) + Li (for task 7)

To calculate the project duration, we sum up the duration of all tasks:
Project Duration = Ti (for task 1) + Ti (for task 2) + Ti (for task 3) + Ti (for task 4) + Ti (for task 5) + Ti (for task 6) + Ti (for task 7)

b) To calculate the manpower cost for the initial project, we need to multiply the total labor power by the wage rate (£15/hr):
Manpower Cost = Total Labor Power * Wage Rate

If the project has to be completed in 20 days, we need to calculate the labor power required to meet this deadline. This can be done by dividing the total quantity of work by the project duration (20 days):
Suggested Labor Power = Total Quantity of Work / Project Duration

To compare the solutions, we can calculate the total labor cost for the initial project using the suggested labor power:
Total Labor Cost = Suggested Labor Power * Wage Rate

c) To calculate how long the project should last before it triples its expenses, we need to consider the initial investment (£47,500) and the additional costs per day (5%).

Let's denote the number of days as D.

After D days, the expenses will be:
Total Expenses = Initial Investment + (5% of Initial Investment) * D

To find out when the expenses triple, we can set this expression equal to triple the initial investment:
3 * Initial Investment = Initial Investment + (5% of Initial Investment) * D

Solving for D will give us the number of days the project should last.

d) To prepare the appropriate graph, we can plot the data points representing the quantity of work (Qi) on the x-axis and the number of workers required (Li) on the y-axis.

Using the least squares method, we can fit a straight line to the data points. This line represents the best fit to the data.

Once we have the equation of the line of best fit, we can substitute Li = 5 into the equation to estimate the value of Qi. The corresponding value of Qi will give us the estimated quantity of work for that task.

To find the duration in days, we can refer to the given duration (Ti) for that task.

e) Effective judgments have been made in relation to the choice of the total labor cost required for the project in Question b). This means that the suggested labor power and the total labor cost for the initial project were calculated based on the specific requirements and constraints of the project.

f) To check the validity of the estimated law in Question d), we can calculate the Pearson Correlation Coefficient between the quantity of work (Qi) and the number of workers required (Li).

The Pearson Correlation Coefficient measures the strength and direction of the linear relationship between two variables. If the coefficient is close to 1 or -1, it indicates a strong positive or negative linear relationship, respectively. If the coefficient is close to 0, it indicates no or weak linear relationship.

Calculating the Pearson Correlation Coefficient will help us assess the validity of the estimated law and determine the strength of the relationship between Qi and Li.

g) to comment critically on how good we expect the forecast of Qi calculated in Question d) to be, we need to consider the quality of the data, the appropriateness of the model used, and any potential uncertainties or variations in the construction project.

If the data used for estimating the line of best fit is reliable and the model assumptions are valid, we can expect the forecast of Qi to be reasonably accurate. However, it's important to note that unforeseen factors or changes in the project may affect the actual results. Therefore, it's always advisable to monitor and update the forecasts as the project progresses.

a)

For Task 2, manpower is required. The manpower required for Task 2 is given by Li = 2.

For Task 4, manpower is required. The manpower required for Task 4 is given by Li = 3.

For Task 1, materials are required. The materials required for Task 1 is given by Mi = 12.

For Task 6, materials are required. The materials required for Task 6 is given by Mi = 12.

For Task 3, equipment is required. The equipment required for Task 3 is given by Ei = 14.

For Task 5, equipment is required. The equipment required for Task 5 is given by Ei = 9.

For Task 7, equipment is required. The equipment required for Task 7 is given by Ei = 6.

To calculate the total labor power, simply add up the labor required for each task:

Total labor power = (2+2+3+3+2+1+1) = 14

To calculate the project duration, add up the duration of each task:

Project duration = (3+5+7+5+3+2+2) = 27 days

b)

To calculate the manpower cost for the initial project, multiply the total labor power by the wage rate:

Manpower cost = (14 * £15/hr) = £210/hr

If the project has to be completed in 20 days, we need to calculate the required labor power. Assuming all tasks are equally important and have the same multiplied factors for Qi, we can use the formula:

Required labor power = (Total quantity of work / Project duration)

Required labor power = [(12+20+14+10+9+12+6)/(3+5+7+5+3+2+2)] = (83/27) ≈ 3.07

Since labor power cannot be fractional, we round up to 4. Therefore, the suggested labor power in this case would be 4.

To compare and contrast the solutions, we can calculate the total labor cost required for the initial project using the suggested labor power of 4:

Total labor cost = (4 * £15/hr) = £60/hr

We can see that the suggested labor power of 4 reduces the total labor cost required for the initial project.

c)

If an initial account of £47500 is invested for material payments in a construction project with 5% additional costs per day, we need to calculate the number of days it takes for the expenses to triple.

Let x be the number of days it takes for the expenses to triple.

£47500 + (0.05 * £47500 * x) = £47500 * 3

After simplifying and rearranging the equation, we get:

0.05 * £47500 * x = £47500 * 2

0.05 * x = 2

x = 2 / 0.05

x = 40

Therefore, the project should last for 40 days before the expenses triple.

d)

To prepare the appropriate graph, we will plot the quantity of work (Qi) on the x-axis and the number of workers required (Li) on the y-axis.

Using the given data, the plot would look like this:

Qi: 12, 20, 14, 10, 9, 12
Li: 2, 2, 3, 3, 2, 1, 1

Now we can use the least squares method to fit a straight line to the data.

By calculating the equation of the best fit line, we can estimate the value of Qi if Li is 5. We can also find the duration in days for that case.

e)

No information is provided for this question. Please provide more context or specific information.

f)

To check the validity of the estimated law in question d), we can calculate the Pearson correlation coefficient.

The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, with 1 indicating a perfect positive linear relationship, 0 indicating no linear relationship, and -1 indicating a perfect negative linear relationship.

By calculating the Pearson correlation coefficient for the given data, we can determine the validity of the estimated law.

g)

The forecast of Qi calculated in question d) will depend on the accuracy and precision of the data and the appropriateness of the linear relationship assumed. If the data is accurate and the assumption of a linear relationship is valid, then the forecast of Qi can be expected to be relatively good. However, if there is significant variability or non-linearity in the data, then the forecast may not be accurate. It is important to consider the limitations and potential sources of error in the data and the assumptions made when interpreting the forecast of Qi.