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Based on the given shaded region as the feasible region in the graph, at which point(s) is the objective function Z = 3x + 9y maximum?

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Based on the given shaded region as the feasible region in the graph, at which point(s) is the objective function Z = 3x + 9y maximum?

(a) Only point B

(b) Only point C

(c) Only point D

(d) Every point on the line segment CD

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Option : (D)

Points Z = 3x + 9y

A (0, 10)

B (5, 5)

C (15, 15)

D (0, 20)

90

60

180 (Maximum)

180 (Maximum)

Z is maximum 180 at points C (15,15) and D(0, 20).

\(\Rightarrow\) Z is maximum at every point on the line segment CD.

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