Page 4 - LESSON NOTES
P. 4
Minimize Z = x + 2y
Subjected to
x + y ≥ 3
25x + 10y ≥ 50
10x + 20y ≥ 40
x ≥ 0, y ≥ 0
Example: 4
Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the
mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg
and Food Q costs Rs 80/kg. Food P contains 3 units /kg of vitamin A and 5 units /kg of Vitamin B
while food Q contains 4 units /kg of vitamin A and 2 units /kg of vitamin B. Determine the
minimum cost of the mixture?
Answer:
Let the mixture contain x kg of food P and y kg of food Q. Therefore,
x ≥ 0 and y ≥ 0
The given information can be compiled in a table as follows:
The mixture must contain at least 8 units of vitamin A and 11 units of vitamin B.
Therefore, the constraints are
3x + 4y ≥ 8
5x + 2y ≥ 11
Total cost, Z, of purchasing food is, Z = 60x + 80y
The mathematical formulation of the given problem is
Minimize Z = 60x + 80y …….. (1)
