A company produces two types of cowboy hats. A type 1 hat requires twice as much labor time as Type 2. If all the 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 revenue is $8 per type 1 hat and $5 per Type 2 hat. a. Use the graphical solution to determine the number of hats of each type that maximizes the revenue. b. Determine the shadow price of the production capacity (in terms of Type 2 hat) and range for which is applicable. c. If the daily demand limit on the Type 1 hat is decreased to 120, use the shadow price to determine the corresponding effect on optimal revenue. d. What is the shadow price of the market share of the Type 2 hat? By how much can the market share be increased while yielding the computed worth of unit. e. Determine the optimality range for the unit revenue ratio of the two types of hats that will keep the current optimum unchanged. f. Using the information in (b), will the optimal solution change if the revenue per unit is the same for two types?