On most university campuses students contracted by academy d

On most university campuses students contracted by academy department to the errand such as answering the phone and typing.the need for such service fluctuates during work hours (8am to 5pm). in the IE department , the mininum number of students needed is 2 between 8am to 10 am , 3 between 10.01am and 11am, 4 between 11:01am and 1pm and 3 between 1;01pm and 5pm.each students is allotted 3 consecutive hours (except for those starting at 3:01, whowork for 2 hours andwho  those start at 4:01, who work for one hour). because of thier flexible schedule, students can usually report to work at any hour during the work day, except that no students want to start working at lunch time (12noon). Determine the miminum number of esteudents the IE department should employa and specify the time of the day at which they should report to work.

Solution

between 8 to 10 AM S>=2

between 10.01 to 11 AM S>=3

between 11:01am and 1pm S >=4

between 1;01pm and 5pm S>=3

students can work for 3 consecutive hours except for

thoe who start at 3:01 they get 2 hours and those who start at

4;01 they get 1 hour

the first shift is for 2 hours from 8 to 10 in the morning so the IE department hire 2 studnets(minimum) for this shift.

the second shift is from 10:01 to 11 AM and IE department require 3 studnets they already have 2 from the first shift as they still have 1 hour left so they\'ll hire 1 studnet form this shift.

for the 3rd shift 11:01 to 1 PM they need 4 students they they are left with 1 fromt the previous shift so they\'ll hire 3 more.

from 1:01 to 5 PM the IE dept. needs 3 students who can work till 2 PM

so for 2:01 to 5 PM they need another 3 students

therefore the minimum number of studnets that the IE department needs to hire is 9