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(A) Let the company manufacture $x$ souvenirs of type $A$ and $y$ souvenirs of type $B$.The given information can be compiled in a table as follows:Pr

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$8$ of type $A$ and $20$ of type $B$

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(A) Let the company manufacture $x$ souvenirs of type $A$ and $y$ souvenirs of type $B$.The given information can be compiled in a table as follows:ProcessType $A$Type $B$AvailabilityCutting (min)$5$$8$$200$Assembling (min)$10$$8$$240$The constraints are:$5x + 8y \leq 200$$10x + 8y \leq 240 \implies 5x + 4y \leq 120$$x, y \geq 0$Objective function to maximize profit $Z = 5x + 6y$.The feasible region is bounded by the corner points $O(0,0)$,$A(24,0)$,$B(8,20)$,and $C(0,25)$.Evaluating $Z$ at corner points:Corner Point$Z = 5x + 6y$$A(24,0)$$5(24) + 6(0) = 120$$B(8,20)$$5(8) + 6(20) = 40 + 120 = 160$$C(0,25)$$5(0) + 6(25) = 150$The maximum profit is $Rs. 160$ at $(8, 20)$. Thus,the company should manufacture $8$ souvenirs of type $A$ and $20$ souvenirs of type $B$.

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