Children have been invited to a birthday party. It is necessary to give them return gifts. For the purpose, it was decided that they would be given pens and pencils in a bag. It was also decided that the number of items in a bag would be atleast 5 . If the cost of a pen is $₹ 10$ and cost of a pencil is ₹5, minimize the cost of a bag containing pens and pencils. Formulation of LPP for this problem is

Question

Children have been invited to a birthday party. It is necessary to give them return gifts. For the purpose, it was decided that they would be given pens and pencils in a bag. It was also decided that the number of items in a bag would be atleast 5 . If the cost of a pen is $₹ 10$ and cost of a pencil is ₹5, minimize the cost of a bag containing pens and pencils. Formulation of LPP for this problem is, Minimize $\mathrm{C}=5 \mathrm{x}+10 \mathrm{y}$ subject to $\mathrm{x}+\mathrm{y} \leq 10$, $x \geq 0, y \geq 0$, Minimize $C=5 x+10 y$ subject to $x+y \geq 10$, $\mathrm{x} \geq 0, \mathrm{y} \geq 0$, Minimize $\mathrm{C}=5 \mathrm{x}+10 \mathrm{y}$ subject to $\mathrm{x}+\mathrm{y} \geq 5$, $x \geq 0, y \geq 0$, Minimize $\mathrm{C}=5 \mathrm{x}+10 \mathrm{y}$ subject to $\mathrm{x}+\mathrm{y} \leq 5$, $x \geq 0, y \geq 0$

MARKS App · Accepted Answer

Let the no. of pencils in a bag be $x$ Let the no. of pens in a bag be $y$. There should be at least 5 items in a bag $\therefore$ we have $\mathrm{x}+\mathrm{y} \geq 5$ cost of pencils in a bag $=₹ 5 \mathrm{x}$ cost of pens in bag $₹ 10 \mathrm{y}$ $\therefore$ Total cost of a bag $=5 \mathrm{x}+10 \mathrm{y}$, The total cost has to minimized $\therefore$ Objective function is minimize $C=5 x+10 y$ subject to $x+y \geq 5, x \geq 0, y \geq 0$

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