A farmer wishes to enclose two identical rectangular plots of land, each having an area of 1200 m, as shown. The outer boundary requires a taller fence that costs $6 per linear metre. The shorter partition fence (dotted line) between the two plots costs $4 per linear metre. If 10 m < x < 40 m, determine the minimum cost for the farmer to fence the boundary and the partition. Round your answer to the nearest dollar.