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Centre of Ellipse

The vertices ...

Question

The vertices of a closed-convex polygon representing the feasible region of the objective function $f = 5 x + 3 y$ , are (0,0), (3,0), (3,1), (1,3) and (0,2). Find the maximum value of the objective function.

A

6

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B

18

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C

14

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D

15

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Solution

The correct option is B 18
Objective function $f = 5 x + 3 y$
The vertices of the convex polygon are (0,0), (3,0), (3,1), (1,3) and (0,2).
The maximum value attains at (3,1).
Therefore, maximum value = $5 \times 3 + 3 \times 1 = 15 + 3 = 18$

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