Dendrites receive and process signals from other neurons. The range of signal intensities that can be robustly distinguished by dendrites is quantified by the dynamic range. We investigate the dynamic range and information transmission efficiency of dendrites in relation to dendritic morphology. We model dendrites in a neuron as multiple excitable binary trees connected to the soma where each node in a tree can be excited by external stimulus or by receiving signals transmitted from adjacent excited nodes. It has been known that larger dendritic trees have a higher dynamic range. We show that for dendritic tress of the same number of nodes, the dynamic range increases with the number of somatic branches and decreases with the asymmetry of dendrites, and the information transmission is more efficient for dendrites with more somatic branches. Moreover, our simulated data suggest that there is an exponential association (decay resp.) of overall relative energy consumption (dynamic range resp.) in relation to the number of somatic branches. This indicates that further increasing the number of somatic branches (e.g. beyond 10 somatic branches) has limited ability to improve the transmission efficiency. With brain-wide neuron digital reconstructions of the pyramidal cells, 90% of neurons have no more than 10 dendrites. These suggest that actual brain-wide dendritic morphology is near optimal in terms of both dynamic range and information transmission.