Please solve the following Operational Research problem. Please show all work and please do all parts thank you.

Problem 4.(20 points. Nike produces two types of cowboy hats. A type 1 hat requires twice as much labor time as a type 2. If the all available labor time is dedicated to Type 2 alone, the company can produce a total of 400 Type 2 hats a day. The respective market limits for the two types are 150 and 200 hats per day. The profit is $8 per Type 1 hat and $5 per Type 2 hat. Determine the number of hats of each type that would maximize profit. (Build the mathematical model, but it is not required to find the optimal solution.) Solution