Nowadays, grid-connected photovoltaic (GCPV) system is known as a top leading technology among all resources. However, it still suffers from drastic investment costs. Detailed economic studies should be conducted in this regard to make this technology as gainful as possible. A practical approach is the "optimum economic design", trying to find an electrically possible layout, i.e. number of series modules and parallel strings as well as the inverter number with the highest profit. This problem is inherently an quadratic integer programming owing to the multiplication of two integer variables in its objective function and some technical constraints. This nonlinear problem should be solved by exhaustive search methods, including comparative and evolutionary algorithms (EAs) such as particle swarm optimization (PSO) and genetic algorithm (GA). In this paper, a new formulation based on the definition of new binary variables has been proposed to convert this problem to the binary linear programming (BLP). The provided method finds the global optimum solution in a scale of seconds while EAs have to be run numerous times in a scale of hours to reach a sufficiently good answer. Moreover, although current methodologies are rarely covered GCPV systems with multiple inverter types, this formulation can be easily developed for systems with several inverter types. The simulations of a 1.1 MW power plant system endorse that the output design provided by the proposed method assures 95,000 $ (1.94%) higher profit compared with those presented by GA. The sensitivity analysis, provided for the prototype system by the efficient new algorithm, also unveils it is economically viable for even 52% of the current feed-in tariff, 40% energy generation lower than the estimated value and 1.1 $/W price rise for the initial investment.