Clearly, x ≥ 0,
y ≥ 0 We make the following table from the given data:
Resources
Food
Requirement
I
II
(x)
(y)
Vitamin A
2
1
8
(units/kg)
Vitamin C
1
2
10
(units/kg)
Cost (Rs/kg)
50
70
Since the mixture must contain at least 8 units of vitamin A and 10 units of
vitamin C, we have the constraints:
2x + y ≥ 8
x + 2y ≥ 10
Total cost Z of purchasing x kg of food ‘I’ and y kg of Food ‘II’ is
Z = 50x + 70y
Hence, the mathematical formulation of the problem is:
Minimise
Z = 50x + 70y (1)
subject to the constraints:
2x + y ≥ 8 (2)
x + 2y ≥ 10