a start up business has $30,000 monthly budgeted for payroll and office rent. offices (y) rent for $2000…

a start up business has $30,000 monthly budgeted for payroll and office rent. offices (y) rent for $2000 while each employee on the payroll (x) makes $5000. the number of employees is less than twice the number of offices rented. write a system of inequalities: according to the graph, what is the maximum number of employees possible within the solution region? show this point on the graph.

a start up business has $30,000 monthly budgeted for payroll and office rent. offices (y) rent for $2000 while each employee on the payroll (x) makes $5000. the number of employees is less than twice the number of offices rented. write a system of inequalities: according to the graph, what is the maximum number of employees possible within the solution region? show this point on the graph.

Answer

Explanation:

Step1: Analyze the system of inequalities

The system of inequalities is: $$ \begin{cases} 2000x + 2000y\leq30000\ x < 2y\ y\leq-\frac{5}{2}x + 15\ y>\frac{1}{2}x \end{cases} $$ Simplify the first inequality (2000x + 2000y\leq30000) by dividing each term by (2000) to get (x + y\leq15) or (y\leq - x+15).

Step2: Find the intersection points

  • Inter - section of (x + y=15) and (x = 2y): Substitute (x = 2y) into (x + y=15), we have (2y+y=15), (3y=15), (y = 5) and (x=10).
  • Inter - section of (x + y=15) and (y=\frac{1}{2}x): Substitute (y=\frac{1}{2}x) into (x + y=15), we get (x+\frac{1}{2}x=15), (\frac{3}{2}x=15), (x = 10), (y = 5).
  • Inter - section of (y=-\frac{5}{2}x + 15) and (y=\frac{1}{2}x): Set (-\frac{5}{2}x + 15[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]