Omega Consulting is trying to schedule its staff of professional consultants to meet the expected needs of its clients over the next four quarters. The following numbers of consulting hours will be needed in the coming year: 36000 hours in quarter 1; 42000 hours in quarter 2; 35000 hours in quarter 3; and 39000 hours in quarter 4. At the beginning of quarter 1, Omega employs 65 experienced consultants. Assume that each of Omegas consultants can work up to 625 hours each quarter before going into overtime. Experienced consultants are paid $20,000 per quarter before overtime. Omega can ask any number of its experienced consultants to work overtime at a rate of $50 per additional hour. However, Omega has established a policy that prohibits asking employees to work more than 150 hours of overtime during each quarter. Historical data suggest that about 4% of the companys professional employees quit by the end of each quarter (assume they quit on the last day of the quarter). Unfortunately, Omega has implemented a hiring freeze for the next four quarters. Omega would like to determine a plan that minimizes the total cost of meeting its demands for consulting services over the upcoming four quarters. Use the shell provided in the file GS 2.xlsx to formulate and solve a linear programming model for this staffing problem.

Problem 1
Number of experienced consultants at start of quarter 1	65
Number of regular-time hours each consultant can work each quarter	625
Number of overtime hours each consultant can work each quarter	150
Quarterly regular-time salary for experienced consultants	$20,000
Hourly overtime rate of pay for experienced consultants	$50
Proportion of experienced consultants who quit each quarter	4%
	Quarter 1	Quarter 2	Quarter 3	Quarter 4
Number of experienced consultants at start of quarter
Total number of regular-time hours available to meet quarterly demand
Total number of overtime hours used to meet quarterly demand
Maximum number of overtime hours available to meet quarterly demand
Total number of hours available to meet quarterly demand
Quarterly demand for consulting services (in hours)	36000	42000	35000	39000
Number of experienced consultants at end of quarter
	Quarter 1	Quarter 2	Quarter 3	Quarter 4
Quarterly regular-time compensation
Quarterly overtime compensation
Total quarterly compensation costs
Total cost for planning horizon