SHAIK AASIF AHAMED
Last Activity: 10 Years ago
Hello student,
Let x and y be the number of packets of food P and Q respectively. Obviously
x ≥ 0, y ≥ 0. Mathematical formulation of the given problem is as follows:
Minimise Z = 6x + 3y (vitamin A)
subject to the constraints
12x + 3y ≥240 (constraint on calcium), i.e. 4x + y ≥ 80 ... (1)
4x + 20y ≥460 (constraint on iron), i.e. x + 5y ≥ 115 ... (2)
6x + 4y ≤300 (constraint on cholesterol), i.e. 3x + 2y ≤ 150 ... (3)
x ≥ 0, y ≥ 0 ... (4)
Z is minimum at the point (15, 20). Hence, the amount
of vitamin A under the constraints given in the problem will be minimum, if 15 packetsof food P and 20 packets of food Q are used in the special diet. The minimum amountof vitamin A will be 150 units.
Thanks and Regards
Shaik Aasif
askIITians faculty