An accounting firm must complete three jobs during the next month. Job $1$ will require $500$

hours of work, Job $2$ will require $300$ hours of work, and Job $3$ will require $100$ hours of work.

Currently the firm consists of $5$ partners, $5$ senior employees and $5$ junior employees, each

whom can work up to $40$ hours per month. The dollar amount $($per hour$)$ that the company can

bill depends on the type of the accountant who is assigned to each job is given in the following

table. $($X indicates that a junior employee does not have enough experience to work on Job $1)$

Table $5$: Billing amounts

All jobs must be completed. The firm has also set the following goals listed in the order of

priority:

Goal $1$ : Monthly billings should exceed $$68000.$

Goal $2$ : At most $1$ partner should be hired.

Goal $3$ : At most $3$ senior employees should be hired.

Goal $4$ : At most $4$ junior employees should be hired.

Formulate a GP for this situation.