A dietician wishes to mix together two kinds | vedclass

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Question

(A) Let the mixture contain $x$ $kg$ of food $X$ and $y$ $kg$ of food $Y$.The mathematical formulation of the given problem is as follows:Minimize $Z

Vedclass · Accepted Answer

$112$

Vedclass · Answer

(A) Let the mixture contain $x$ $kg$ of food $X$ and $y$ $kg$ of food $Y$.The mathematical formulation of the given problem is as follows:Minimize $Z = 16x + 20y$ ... $(1)$Subject to the constraints:$x + 2y \geq 10$ ... $(2)$$2x + 2y \geq 12$ (which simplifies to $x + y \geq 6$) ... $(3)$$3x + y \geq 8$ ... $(4)$$x, y \geq 0$ ... $(5)$The feasible region determined by the system of constraints is unbounded.The corner points of the feasible region are $A(10, 0)$,$B(2, 4)$,$C(1, 5)$,and $D(0, 8)$.The values of $Z$ at these corner points are as follows:						Corner point			$Z = 16x + 20y$							$A(10, 0)$			$160$							$B(2, 4)$			$112$							$C(1, 5)$			$116$							$D(0, 8)$			$160$			As the feasible region is unbounded,we check if $16x + 20y Since the line $16x + 20y = 112$ does not pass through the interior of the feasible region,the minimum value is $112$ at $(2, 4)$.Thus,the least cost of the mixture is $Rs. 112$.

Food	Vitamin $A$	Vitamin $B$	Vitamin $C$
$X$	$1$	$2$	$3$
$Y$	$2$	$2$	$1$

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