The heat-rejection system for a condenser of a steam power plant is to be designed for minimum first plus pumping cost. The heat-rejection rate from the condenser is 14MW. The following costs in dollars must be included:

First cost of cooling tower, 800A^0.6, where A =area,m2

Lifetime pumping cost, 0.0005w^3, where w=flow rate of water, kg/s

Lifetime penalty in power production due to elevation of temperature of cooling water, 270t, where t=temperature of water entering the condenser, C

The rate of heat transfer from the cooling tower can be represented adequately by expression q, W=3.7(w^1.2)tA

(a)    determine the minimum lifetime cost

(b)   calculate the optimal values of A and w