Suppose Polaris needs to ensure employee coverage for the following times between $7$am and $4$pm$.$

$7$am$-8$am$=7$; $8$am$-9$am$=7$; $9$am$-10$am$=8$; $10$am$-11$am$=8$; $11$am$-12$pm$=9$; $12$pm$-1$pm$=10$; $1$pm$-2$pm$=10$; $2$pm$-3$pm$=9$; $3$pm$-4$pm$=8$

Employees available for these times include full$-$time workers, working $7$am$-4$pm$,$ and part time workers who can work one of the following, $4-$hour shifts.

$7$am$-11$am; $8$am$-12$pm; $9$am$-1$pm; $10$am$-2$pm; $11$am$-3$pm; $12$pm$-4$pm

All full$-$time employees take their one$-$hour lunch break at $11$am$.$ To ensure part$-$time shifts can be covered, Polaris management limits the number of workers in each of the shifts to no more than $3.$

Determine the how many of each type of shift need to be hired to minimize the number of total employees. The optimal solution will be $17.$

Suppose Polaris is looking to cut costs and wants to minimize the number of full$-$time employees to help reduce benefit expenditures without increasing the total number of employees. Resolve this problem with the new goal and constraint. Discuss both the original and secondary goal recommendations and outcomes. A less than or equal to constraint will make your model more robust for ST$.$

Use Solvertable to see what happens to total employees and FT employees when the required number of workers needed from $11$am$-12$pm ranges from $6-12.$ Think about what increments would be most helpful if you were the manager when building ST$.$