I need help with iii please. In the last paragraph there is a typo. It supposed

Question

I need help with iii please. In the last paragraph there is a typo. It supposed to be 20 houses not 18.

You have decided that for your summer job you are going to manage a group of students who will paint houses to earn money for the summer. As Manager, your paycheck depends on your capability to efficiently schedule the team so that all the houses get painted on time with little, or ideally no. overage on scheduled man-hours. Given that a house requires H man-hours to paint, your team has N houses to paint and P students on the team: Write the expression that relates the number of students that you will need to schedule to finish painting the houses in 12 weeks assuming 40-hour work weeks. If it takes 120 man-hours to paint a house and your team has 20 houses to paint, how many students do you need to hire to paint the houses in 12 weeks assuming 40-hour workweeks? A friend of yours, Bionka, managed a College Pro Painting team last summer and tells you that since every student is not as efficient as you may expect combined with the fact that the neighborhood you're covering has both small and large houses, the number of man-hours to paint a house. H, is not exactly 120. Instead, she tells you that H is equally likely to take anywhere from 100 man-hours to 130 man-hours. Additionally, Bionka hints that not all of your workers show up as expected. In fact, during a given week a man-day (8 hours) of work is lost on the average of 1.2 times. Fill in the following probability tables: Let R = Number of times 8 man-hours (a man-day) will be lost in a week Recall that you have 12 weeks to paint these houses. Considering the two 'risks of uncertainty' characterized by the above tables that contain more realistic information regarding the number of man-hours that will probably be required to paint the 18 houses and the number of man-days of work that will probably be lost per week for each of the 12 weeks, how many students should you recruit to be most efficient? Briefly explain your answer.

Explanation / Answer

Given:   H = Man-hours to paint house

              N = Number of Houses

               P = Number of students in ateam(to paint)

(i)Given :

Total time required to paint = 12 weeks to paint     

Work done by a painter in each week = 40 man-hours/week/painter

          Total number of man-hours to finish all houses = N * H ------(i)

            Total man-hours available in 12 weeks = P * 40 * 12      ------(ii)

Equate both of these expressions, after equating

N*H=P*40*12

Calculate P, from the above expression

P = (N * H) / 480

(ii) Given, Man-hours to paint house (H) = 120 man-hours/house

             Number of Houses (N) = 18 houses

            Put the values in the above given formula,

P = (N * H) / 480

P = (18 * 120)/ 480 = 4.5

A person cannot be in decimal form.Therefore, it needs 5 painters to paint.

iii)   Assume a uniform distribution

H

100

120

140

160

P(H)

.25

.25

.25

.25

Number of Houses (N) = 18 houses

Calculate the number of man-hours to finish =

.25(18)(100) + (.25)(18)(120) + (.25)(18)(140) + (.25)(18) (160)

         = 450 + 540 + 630 + 720

         =   2340 man-hours

Apply Poisson Distribution for number of times 8 man-hours lost per week

R

0

1

2

3

4

5

P(R)

.1496  

.2842

.2700

.1710

.0812

.0309

If we choose P(X <= 4) days

Man-hours lost per week = 8 man-hours/day * 4 days = 32 man-hours/week

Over 12 weeks, man-hours lost that will need to be made up are =32 man-hours/week * 12 weeks

      = 384

Now, add this to the man-hours to finish houses: 2340 + 384 = 2724 man-hours

Substitute into formula for painters:

P = (N * H) / 480

            P = 2724 / 480 = 5.675     

A person cannot be in decimal form.Therefore, it needs 6 painters to paint.

H

100

120

140

160

P(H)

.25

.25

.25

.25

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