Nolan Industries manufactures water filters$/$purifiers that attach to a kitchen faucet. Each purifier consists of a housing unit that attaches to the faucet and a $60-$day filter $($sold separately$)$ that is inserted into the housing. Past records indicate that on average, the number of filters produced per week should be at least $600.$ It takes $20$ minutes to make and assemble each filter and $40$ minutes for each housing. The manufacturing facility has at least $16,000$ minutes per week for making and assembling these units, but due to certain parts supply constraints, the number of housing units per week can be at most $800.$ If manufacturing costs $($for material and labor$)$ are $$6\mathrm{.}10$ for each filter and $$8\mathrm{.}70$ for each housing unit, how many of each should be produced to minimize weekly costs?