Q. The mayor of Cambridge, Colorado, wanting to be environment progressive decides to implement a recycling plan. All residents of the city will receive a special three part bin to separate their glass, plastic also aluminium, also the city will be responsible for picking up the materials. A young city also regional planning graduate, Michael Duffy, has been hired to manage the program of recycling. Later than 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 also subdivisions in the city also surrounding community. To stimulate residents of some areas to have their pickups planned 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 also 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. Elucidate how much slack does your schedule generate for each day?

c. Assume Duffy can smooth the requirements further through greater tax incentive. Requirements then will be eight collectors on Monday also seven on the other days of the week. Elucidate how many collectors will be needed now? Does smoothing of requirements have capital investment implications? If so, Illustrate are they?