A toy workshop that specializes in crafting three unique types of toys, all

manufactured using the same production machinery. The anticipated

annual demands and typical order sizes for each toy are detailed in the

workshiop's records. With an annual availability of $2,000$ production hours,

the workshop maintains a $10\%$ capacity cushion to account for preventive

maintenance, unexpected breakdowns, and other unforeseen events. How

many production machines must the workshop have to meet these

circumstances and ensure the smooth execution of toy manufacturing?