A company needs to hire four types of employees: Software Developers $($SD$),$ Data Analysts $($DA$),$ and Marketing Specialists $($MS$).$ The profit generated by each type of employee per month is $$5000$ for SD$,$ $$4000$ for DA$,$ and $$3000$ for MS$.$ The company has constraints on the total number of avhours, office space, and computer resources. Each SD requires $160$ work hours, $2$ units of and $1$ computer. Each DA requires $120$ work hours, $1$ unit of office space, and $1$ computer. Each MS requires $80$ work hours, $1$ unit of office space, and $1$ computer. There are $1500$ working hours, $10$ units of office space, and $8$ computers available. In the hiring process, the company is required to hire at least $1$ MS$.$ The company wants to maximize its monthly profit. Using the decision variables $($SD: $x1,DA$:$x2,$ MS: $x3),$ find the most accurate Linear Programming model for this scenario.

Select one:

$$ a$.,$ maximize $Z=50001+40002+30003$

subject to:

$1601+1202+8031500$

$2x1+x2+x310$

$x1+x2+x38$

$x31$

$x1,x2,x30$

b$.$

minimize $Z=50001+40002+30003$

subject $to$:

$1601+1202+8031500$

$22+x2+x310$

$x1+x2+x38$

$x31$

$x1,x2,x30$

c$.$ minimize $Z=40001+50002+20003$