Old Pueblo Engineering Contractors creates six$-$month $$rolling$$ schedules, which are recomputed monthly. For competitive reasons $($it would need to divulge proprietary design criteria, methods, and so on$),$ Old Pueblo does not subcontract. Therefore, its only options to meet customer requirements are $(1)$ work on regular time; $(2)$ work on overtime, which is limited to $30$ percent of regular time; $(3)$ do customers$$ work early, which would cost an additional $$5$ per hour per month; and $(4)$ perform customers$$ work late, which would cost an additional $$10$ per hour per month penalty as provided by their contract.

Old Pueblo has $25$ engineers on its staff at an hourly rate of $$30.$ The overtime rate is $$45.$ Customers$$ hourly requirements for the six months from January to June are