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$$y_i=\sum_j a_{ij} x_j\geqslant \prod_j x_j^{a_{ij} }$$ by Jensen inequality for logarithm. Now multiply bytake the product over $i=1,2,\dots,n$.
$$y_i=\sum_j a_{ij} x_j\geqslant \prod_j x_j^{a_{ij} }$$ by Jensen inequality for logarithm. Now multiply by $i=1,2,\dots,n$.
$$y_i=\sum_j a_{ij} x_j\geqslant \prod_j x_j^{a_{ij} }$$ by Jensen inequality for logarithm. Now take the product over $i=1,2,\dots,n$.
