The mayor of Cambridge, Colorado, wanting to be environmentally progressive, decides to implement a recycling plan. All residents of the city will receive a special three part bin to separate their glass, plastic and aluminum, and the city will be responsible for picking up the materials. A young city and regional planning graduate, Michael Duffy, has been hired to manage the recycling program. After carefully studying the city's population density, Duffy decides that the following numbers of recycling collectors will be needed:
Day M T W Th F S Su
Requirements 12 7 9 9 5 3 6
The requirements are based on the populations of the various housing developments and subdivisions in the city and surrounding communities. To motivate residents of some areas to have their pickups scheduled on weekends, a special tax break will be given.
a. Find the minimum number of recycling collectors required if each employee works 5 days a week and has 2 consecutive days off. Give preference to the S-Su pair when that pair is involved in a tie.
b. Specify the work schedule for each employee. How much slack does your schedule generate for each day?
c. Suppose Duffy can smooth the requirements further through greater tax incentives. The requirements then will be eight collectors on Monday and seven on the other days of the week. How many collectors will be needed now? Does smoothing of requirements have capital investment implications? If so, what are they?