Two food supplements A and B contain different amounts of protein and fat
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
Two food supplements A and B contain different amounts of protein and fat. Their nutritional data and cost per packet are:
• Supplement A: 6 units protein, 4 units fat, cost Rs 6 per packet.
• Supplement B: 4 units protein, 8 units fat, cost Rs 5 per packet.
A diet must provide at least 48 units of protein and at least 32 units of fat per day at minimum cost.
Using the number of packets of each supplement as variables, proceed as follows.
(i) Construct the two constraint inequalities for nutrient requirements along with the non-negativity restrictions.
(ii) Write the cost function to be minimised.
(iii) Draw the feasible region corresponding to part (i) and locate all its corner points.
(iv) Evaluate the cost at every corner point and obtain the least daily cost. State the optimal number of packets of each supplement that should be consumed.