$A$ diet of a sick person must contain at least $4000$ units of vitamins,$50$ units of proteins,and $1400$ calories. Two foods $A$ and $B$ are available at a cost of ₹ $4$ and ₹ $3$ per unit respectively. If one unit of $A$ contains $200$ units of vitamins,$1$ unit of protein,and $40$ calories,while one unit of food $B$ contains $100$ units of vitamins,$2$ units of protein,and $40$ calories,formulate the problem so that the diet is the cheapest.

• A
  $200x + 100y \geq 4000, x + 2y \geq 50, 40x + 40y \geq 1400, x \geq 0, y \geq 0, \text{Minimize } z = 4x + 3y$
• B
  $400x + 200y \geq 100, x + 2y \geq 50, 40x + 40y \geq 1400, x \geq 0, y \geq 0, \text{Minimize } z = 4x + 3y$
• C
  $100x + 200y \geq 4000, x + 2y \geq 50, 40x + 40y \geq 1400, x \geq 0, y \geq 0, \text{Minimize } z = 4x + 3y$
• D
  None of the above