 Solution

The dual is $\boxed{D:\min b^{T}y\text{ subject to }{A}^{T}y\ge c,y\ge 0}$. For feasible points $c^{T}x\le y^{T}Ax\le y^{T}b$, so its feasible objectives bound the primal objective from above. This is weak duality with the given maximization convention.