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The solution

$$\begin{gathered} Solution: \\ Let the floor area be x m^2. \\ Production line = x -\frac{2x}{3} =\frac{x}{3} \\ Total area of office space and canteen is given as \frac{3}{5 } out of remaining area \\ \Rightarrow \frac{3}{5} \left(\frac{x}{3}\right) = \frac{x}{5} \\ Warehouse space = \frac{x}{3}-\frac{x}{5}= \frac{5x-3x}{15} = \frac{2x}{15} \\ \Rightarrow \frac{2x}{15} = 2000 m^2 \Rightarrow x = 15000 \\ Production line = \frac{2x}{3}= \frac{2 x 15000}{3}= 2 x 5000 = 10,000m^2 . \end{gathered}$$