By the above, we know p x i w i   \cdot \mathbf {x_{i}} \geq w_{i}} for all i and p x i > w i   \cdot \mathbf {x_{i}} >w_{i}} for some i. Summing, we find: Because Y  } } is profit maximizing, we know j p y j j p y j  \mathbf {p} \cdot y_{j}^{*}\geq \Sigma _{j}p\cdot y_{j}} , so i p x i > j p y j  \mathbf {p} \cdot \mathbf {x_{i}} >\Sigma _{j}\mathbf {p} \cdot \mathbf {y_{j}} } .
পূৰ্বৰ তৰ্কৰ পৰা আমি জানো, প্ৰত্যেক i ৰ বাবে p ⋅ x i ≥ w i   \cdot \mathbf {x_{i}} \geq w_{i}} আৰু কিছু i ৰ বাবে p ⋅ x i > w i   \cdot \mathbf {x_{i}} >w_{i}} ।