A diet of a sick person must contain atleast 4000 unit of vitamins, 50 unit of proteins and 1400 calories. Two foods \(\mathrm{A}\) and \(\mathrm{B}\) are available at cost of ₹ \(4\) and ₹ \(3\) per unit respectively. If one unit of A contains 200 unit of vitamins, 1 unit of protein and 40 calories, while one unit of food B contains 100 unit of vitamins, 2 unit of protein and 40 calories. Formulate the problem, so that the diet be cheapest.

1. A \(200 x+100 y \geq 4000, x+2 y \geq 50\)
   \(40 x+40 y \geq 1400, x \geq 0\) and \(y \geq 0\)
   \(O . F z=4 x+3 y\)
2. B \(400 x+200 y \geq 100, x+2 y \geq 50\)
   \(40 x+40 y \geq 1400, x \geq 0\) and \(y \geq 0\)
   O. \(F z=4 x+3 y\)
3. C \(100 x+200 y \geq 4000, x+2 y \geq 50\),
   \(40 x+40 y \geq 1400, x \geq 0\) and \(y \geq 0\)
   O. \(F z=4 x+3 y\)
4. D None of the above