A production manager can use two types of machines to produce products: a new model machine and an old model machine. A new model machine can produce up to $200$ products a day and an old model machine, up to $150$ products a day. Every product is sold at NIS $20.$ The daily wage of a worker who operates a new model machine is $255$ NIS, and the daily wage of a worker who runs an old model machine is $212\mathrm{.}5$ NIS. Each worker is attached to their machine during the working day and requires exactly one worker per machine. Moreover, it is known that the number of new model machines should be at least like the number of old model machines. An inspector who inspects the operation of all machines once a day needs one hour to test each new model machine and $40$ minutes to test each old model machine. The inspector can work up to $8\mathrm{.}5$ hours a day.