Food $\text{X}$ contains $6$ units of Vitamin $\text{D}$ per gram and $7$ units of Vitamin $\text{E}$ per gram and cost is Rs $12$ per gram. Food $\text{Y}$ contains $8$ units of vitamin $\text{D}$ per gram and $12$ units of Vitamin $\text{E}$ per gram and cost is Rs $20$ per gram. The daily minimum requirements of vitamin $\text{D}$ and $\text{E}$ are $100$ units and $120$ units respectively.
Suppose $x$ is quantity (in gram) of food $\mathrm{X}$, $y$ is quantity (in gram) of food $\mathrm{Y}$ .
Answering the following question based on the above paragraph given.
The dual of the formulated LPP is:
| $\text { Max } Z =100 u+120 v$ |
| $\text { s.t. }$ |
| $ \quad \quad 6 u+7 v \leqslant 12$ |
| $ \quad \quad 8 u+12 v \leqslant 20$ |
| $\quad \quad u, v \geqslant 0$ |
| $\text { Max } Z =12 u+20 u$ |
| $\text { s.t. }$ |
| $\quad \quad 6 u+7 v \leqslant 100$ |
| $\quad \quad 8 u+12 v \leqslant 120$ |
| $\quad \quad u, v \geqslant 0$ |
| $\text { Max } Z =100 u+120 v $ |
| $\text { s.t. }$ |
| $\quad \quad 6 u+7 u \leqslant 12$ |
| $\quad \quad 8 u+7 v \leqslant 20$ |
| $\quad \quad u, v \text { are unrestricted }$ |
| $\text { Max } Z=100 u+120 u$ |
| $\text { s.t. }$ |
| $\quad \quad 6 u+7 v \geqslant 12$ |
| $\quad \quad 8 u+12 v \geqslant 20$ |
| $\quad \quad u, v \geqslant 0$ |
