Since water is heavier to carry than an empty pail, it should take longer to walk when carrying water than when not. Suppose travel time is proportional to distance traveled and that travel takes w ( w > 0) times as long when carrying water than when carrying an empty pail. (For example, if time = 2 Ã- distance, time with water = 2 w Ã- distance.) (a) Formulate a nonlinear programming problem to determine the location of the tavern that minimizes the AM travel time ONLY using the HEAVY WATER SCENARIO. (b) Let v = 5 , a = 3 , L = 8 , w = 2. Solve the AM problem using golden section search. (The initial interval of uncertainty is [0 , L ].) Set the tolerance equal to 0.001