Problem $6.(20$ points$)$

Flash Fasttrack $($associate dean of janitorial services at Wombat University$)$ must schedule

the regular maintenance by his janitorial engineers. There are two crews: sweeping crew

and waxing crew. Union rules prohibit sweepers from waxing and waxers from sweeping.

A building$$s floors must first be swept before they can be waxed. Flash must schedule the

order in which maintenance crews will visit each of Wombat U$$s six buildings. He wished

to minimize the sequence$$s total completion time. Times required to sweep and wax each

building are as follows:

Building Sweeping Time $($Hours$)$ Waxing Time $($Hours$)$

Astronomy $1810$

Biology $89$

Chemistry $2613$

Drama $1516$

English $1720$

Foreign language $1217$

a$.(12$ pts$)$ Schedule the crews through the buildings.

b$.(4$ pts$)$ When will the waxing crew start and stop work in the chemistry building?

c$.(4$pts$)$ During the schedule, for how much time are sweepers and waxers available for

other activities?