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A port operator would like to optimize port operation by adjusting docking fee (P). In doing so, the operator considers two objectives.
A port operator would like to optimize port operation by adjusting docking fee (P). In doing so, the operator considers two objectives. The first objective is to increase total revenues and hence maximize gross revenues. The second objective is to maximize profits. Currently, P is set at $2000 per million tons of freight loaded (or unloaded), and the volume of freight is 2 million tons per week. The operator feels that demand is sensitive to both the docking fee charged and the process time for loading/unloading, and has estimated the following demand function:
V=20−4t−0.004????
W here, V = demand or volume in million tons per week
t = loading/unloading time (in days)
(a) If service time t is currently constant at 2 days, what docking fee should the port operator charge to maximize total revenues? What is the corresponding level of demand and net change in revenue?
(b) After careful analysis of port performance, it is estimated that service time is given by the following function: t=1.2+0.6V
Assuming that the system will adjust to a new equilibrium after any change in P, find the value of P that maximizes total revenues. Is this higher or lower than the optimum docking fee found in Part (a)?
(c) Suppose that total costs depend only on demand, and is estimated as follows: C=12,000+1,000V
What docking fee should the port operator charge to maximize profits considering the process time function from Part (b)?
