A merchant plans to sell two types of persona | vedclass

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Question

(A) Let the merchant stock $x$ desktop models and $y$ portable models.The cost of a desktop model is $Rs.\,25000$ and of a portable model is $Rs.\,400

Vedclass · Accepted Answer

$200$ desktop,$50$ portable

Vedclass · Answer

(A) Let the merchant stock $x$ desktop models and $y$ portable models.The cost of a desktop model is $Rs.\,25000$ and of a portable model is $Rs.\,40000$.Given that the merchant can invest a maximum of $Rs.\,70$ lakhs $(Rs.\,70,00,000)$:$25000x + 40000y \leq 7000000$Dividing by $5000$,we get:$5x + 8y \leq 1400$ ... $(1)$The total monthly demand of computers will not exceed $250$ units:$x + y \leq 250$ ... $(2)$Also,$x \geq 0$ and $y \geq 0$ ... $(3)$The profit function to be maximized is:$Z = 4500x + 5000y$We find the corner points of the feasible region by solving the equations $5x + 8y = 1400$ and $x + y = 250$:From $x + y = 250$,$y = 250 - x$. Substituting in $(1)$:$5x + 8(250 - x) = 1400$$5x + 2000 - 8x = 1400$$-3x = -600 \implies x = 200$$y = 250 - 200 = 50$The corner points of the feasible region are $(0, 0)$,$(250, 0)$,$(200, 50)$,and $(0, 175)$.Evaluating $Z$ at these points:Corner Point$Z = 4500x + 5000y$$(0, 0)$$0$$(250, 0)$$4500(250) = 1125000$$(200, 50)$$4500(200) + 5000(50) = 900000 + 250000 = 1150000$$(0, 175)$$5000(175) = 875000$The maximum profit is $Rs.\,1150000$ at $(200, 50)$.Thus,the merchant should stock $200$ desktop models and $50$ portable models.

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