The present paper presents an algorithm to find optimum time- cost trade off pairs in a fixed charge linear capacitated transportation problem with enhanced flow. Sometimes, situations arise where either reserve stocks have to be kept at supply points say, for emergencies, or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. Moreover, sometimes a fixed charge ( like set up cost for machines, landing fees at an airport, cost of renting a vehicle ) is also associated with every origin that gives rise to fixed charge problem. In this paper a special class of transportation problem is studied, where the total transportation flow is enhanced to a specified level. A numerical example is given to illustrate the developed algorithm.