$2-16.$ Wild West produces two types of cowb his pleasure from both work and play? time as a Type $2.$ If all the available labor hats. A Type $1$ hat requires twice as much labor can produce a total of $400$ Type $2$ labor time is dedicated to Type $2$ alone, the company and Type $2$ are $150$ and $200$ hats per $2$ hats a day. The respective market limits for Type $1$ $$5$ per Type $2$ hat. Determine the number respectively. The profit is $$8$ per Type $1$ hat and