CASE STUDY CHALLENGE
Linear Programming: Diet Optimization
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 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:
Answer the following:
| (i) | Identify and write all the constraints which determine the given feasible region in Figure-2. | [2] |
| (ii) | If the objective is to minimize cost Z = 16x + 20y, find the values of x and y at which cost is minimum. Also, find minimum cost assuming that minimum cost is possible for the given unbounded region. | [2] |