Let x & y denotes the units of Food 1 & 2 to be purchased respectively.
According to question, the above data can be expressed as-
Minimise: Z = 5x + 7y …Objective function
Subject to Constraints:
2x + y ≥ 8
x + 2y ≥ 10
x, y ≥ 0
On plotting the half planes the unbounded feasible region with corners A, E & D is obtained.
Z is going to be optimized only at the corner points.
So we check value of z only at corner points.
A (0,8) z = 5(0) + 7(8) = 56
B (2,4) z = 5(2) + 7(4) = 38 (min.)
C (10,0) z = 5(10) + 7(0) = 50
As per the graph, the unbounded region has a new equality,
5x + 7y < 38
This inequality has no common point with the previous mentioned equations,
Thus, the minimum cost is Rs. 38 when 2 units of Food 1 and 4 units of Food 2 are purchased.
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