Corner points of the bounded feasible region | vedclass

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(B) To find the minimum and maximum values of the objective function $z = 8x + 12y$,we evaluate $z$ at each corner point:$1. 	ext{At } (0,4): z = 8(0

Vedclass · Accepted Answer

$(i) (0,4), (ii) (12,16), (iii) 288, (iv) 48$

Vedclass · Answer

(B) To find the minimum and maximum values of the objective function $z = 8x + 12y$,we evaluate $z$ at each corner point:$1. 	ext{At } (0,4): z = 8(0) + 12(4) = 48$$2. 	ext{At } (6,0): z = 8(6) + 12(0) = 48$$3. 	ext{At } (12,0): z = 8(12) + 12(0) = 96$$4. 	ext{At } (12,16): z = 8(12) + 12(16) = 96 + 192 = 288$$5. 	ext{At } (0,10): z = 8(0) + 12(10) = 120$Comparing these values:- The minimum value is $48$,which occurs at both $(0,4)$ and $(6,0)$.- The maximum value is $288$,which occurs at $(12,16)$.Matching the given requirements:$(i)$ Minimum value occurs at $(0,4)$ (or $(6,0)$).$(ii)$ Maximum value occurs at $(12,16)$.$(iii)$ Maximum of $z$ is $288$.$(iv)$ Minimum of $z$ is $48$.Thus,option $(B)$ is the correct match.

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