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The maximum value P = 3x + 4y subjected ...

The maximum value `P = 3x + 4y` subjected to the constraints `x + y le 40, x + 2y le 60, x ge 0 and y ge 0` is

A

120

B

140

C

100

D

160

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The correct Answer is:
B
Given, `P = 3x + 4y`

The graph has been drawn from given constrants and maximum value of P will be at A or B or C
`P_(A) = P_((o,30))`
`= 3 xx 0 + 4 xx 30 = 120`
`P_(B) = P((20, 20))`
` = 3 xx 20 + 4 xx 20 = 140`
and `P_(C) = P((40, 0)) = 3 xx 40 + 0 = 120`
`therefore P_(max) = 140`
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