You are coordinating the construction of a shelter for homeless people. A large number of college students and members of a religious organization have signed up as volunteers for constructing the shelter. About 30% of these volunteers are skilled, but the rest are not. It is estimated that the total number of man-hours required to complete the construction of the shelter is 1200—if all volunteers are skilled. Three times as many unskilled volunteers are required to complete any job compared to skilled volunteers. The average number of hours a skilled volunteer is available is 10/week while unskilled volunteers are available for 15 hours every week.

Explanation:

The plan outlined here makes nearly best use of available resources and job constraints. It results in job completion in about 12 weeks, or 3 months.

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For simplicity, we choose to work 5 hours per day, 5 days a week. Each skilled volunteer will complete their weekly 10 hours by working 2 days. Each unskilled volunteer will complete their 15 hours by working 3 days. Some volunteers will work an "interrupted" schedule that consists of non-consecutive work days. The purpose of this is to provide compliance with job site limitations, volunteer hour limitations, and to maximize continuity of communication as the job progresses.

A weekly schedule along these lines is shown in the attachment. It has 2 skilled volunteers and 6 or 7 unskilled volunteers on site each day. The ratio of skilled to unskilled volunteers is 31% : 69%. Each works the maximum number of hours for their skill level.

The net result is that 50 skilled hours and 165 unskilled hours are worked each week.

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We assume the wording "three times as many unskilled volunteers are required to complete any job compared to skilled volunteers" means that 3 unskilled hours are equivalent to 1 skilled hour. (An alternative interpretation is that 45 hours of unskilled labor is equivalent to 10 hours of skilled labor.)

Using this assumption, job completion occurs at the equivalent rate of ...

  50 +165/3 = 105 . . . equivalent skilled hours per week

The total job requirement of 1200 skilled hours can be met in 12 weeks' time, well within the 6-month desired completion period. (Even using the alternate interpretation of labor equivalent, the job can be done in 14 weeks.)

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In any given week, the 5 skilled volunteers are designated s1–s5, and the 11 unskilled volunteers are u1–u11. The days they're scheduled to work are identified by the weekday labels M, T, W, T, F. Skilled volunteer s1 works only Monday and Friday, and is responsible for week-to-week tie-in. Unskilled volunteers u2, u4, u7, u9 get two (2) days off in the middle of each week.

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