31.

A diet of a sick person must contain atleast 4000 unit of vitamins, 50 unit of proteins and 1400 calories. Two foods A and B are available at cost rs. 4 and rs. 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

• $$\begin{gathered} 200\mathrm{x} + 100\mathrm{y} \ge 4000, \mathrm{x} + 2\mathrm{y} \ge 50 \\ 40\mathrm{x} + 40\mathrm{y} \ge 1400, \mathrm{x} \ge 0 \mathrm{and} \mathrm{y} \ge 0 \\ \mathrm{O}. \mathrm{F} \mathrm{z} = 4\mathrm{x} + 3\mathrm{y} \end{gathered}$$

• $$\begin{gathered} 400\mathrm{x} + 200\mathrm{y} \ge 100, \mathrm{x} + 2\mathrm{y} \ge 50 \\ 40\mathrm{x} + 40\mathrm{y} \ge 1400, \mathrm{x} \ge 0 \mathrm{and} \mathrm{y} \ge 0 \\ \mathrm{O}. \mathrm{F} \mathrm{z} = 4\mathrm{x} + 3\mathrm{y} \end{gathered}$$

• $$\begin{gathered} 100\mathrm{x} + 200\mathrm{y} \ge 4000, \mathrm{x} + 2\mathrm{y} \ge 50 \\ 40\mathrm{x} + 40\mathrm{y} \ge 1400, \mathrm{x} \ge 0 \mathrm{and} \mathrm{y} \ge 0 \\ \mathrm{O}. \mathrm{F} \mathrm{z} = 4\mathrm{x} + 3\mathrm{y} \end{gathered}$$

• None of the above

The constraints - x₁ + x₂ $\le$ 1, - x₁ + 3x₂ $\le$ 9, x₁, x₂ > 0 defines on

• bounded feasible space

• unbounded feasible space

• both bounded and unbounded feasible space

• None of the above

By Simpson rule taking n = 4, the value of the integral ${\int }_0^1\frac{1}{1 + {\mathrm{x}}^2}\mathrm{dx}$ is equal to

• 0.788

• 0.781

• 0.785

• None of the above