Question

The month of September is celebrated as the Rashtriya Poshan Maah across the country. Following a healthy and well-balanced diet is crucial in order to supply the body with the proper nutrients it needs. A balanced diet also keeps us mentally fit and promotes improved level of energy. A dietician wishes to minimize the cost of a diet involving two types of foods, food X (x kg) and food Y (y kg) which are available at the rate of ₹ 16/kg and ₹ 20/kg respectively. The feasible region satisfying the constraints is shown in Figure-2. On the basis of the above information, answer the following questions :

Solve the following linear programming problem graphically : Maximise z = 4x + 3y, subject to the constraints x + y ≤ 800 2x + y ≤ 1000 x ≤ 400 x, y ≥ 0.

The maximum value of Z = 4x + y for a L.P.P. whose feasible region is given below is:

Assertion (A): The corner points of the bounded feasible region of a L.P.P. are shown below. The maximum value of Z = x + 2y occurs at infinite points. Reason (R): The optimal solution of a LPP having bounded feasible region must occur at corner points.