Lucy’s Music Store at present employs five full-time employees and three part-time employees. The normal workload is 40 hours per week for full-time employees and 20 hours per week for part-time employees. Each full-time employee is paid $6 per hour for work up to 40 hours per week and can sell five recordings per hour. A full-time employee who works overtime is paid $10 per hour. Each part-time employee is paid $3 per hour and can sell three recordings per hour. It costs Lucy $6 to buy a recording, and each recording sells for $9. Lucy has weekly fixed expenses of $500. She has established the following weekly goals, in order of priority:
■ Goal 1: Sell at least 1600 recordings per week.
■ Goal 2: Earn a profit of at least $2200 per week.
■ Goal 3: Full-time employees should work at most 100 hours of overtime.
■ Goal 4: To promote a sense of job security, the number of hours by which each full-time employee fails to work 40 hours should be minimized.
Use a goal programming model to determine how many hours per week each employee should work.