Question $7.$

Ricky's Record Store now employs five full$-$time employees and three part$-$time employees. The normal workload is $40$ hours per week for full$-$time and $20$ hours per week for part$-$time employees. Each fulltime employee is paid $$6$ per hour for work up to $40$ hours per week and can sell $5$ records per hour. A full$-$time employee who works overtime is paid $$10$ per hour. Each part$-$time employee is paid $$3$ per hour and can$-$sell $3$ records per hour. It costs Ricky $$6$ to buy a record, and each record sells for $$9.$ Ricky has weekly fixed expenses of $$500.$ He has established the following weekly goals, listed in order of priority:

Goal $1$: Sell at least $1,600$ records per week.

Goal $2$: Earn a profit of at least $$2,200$ per week.

Goal $3$: Full$-$time employees should work at most $100$ hours of overtime.

Goal $4$: To increase their sense of job security, the number of hours by which each full$-$time employee fails to work $40$ hours should be minimized.

Formulate a goal programming model that could be used to determine how many hours per week each employee should work.