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(A) Let $x$ be the number of pieces of Model $A$ and $y$ be the number of pieces of Model $B$.The objective function is to maximize profit $Z = 8000x

Vedclass · Accepted Answer

$12$ pieces of $A$,$6$ pieces of $B$; Max Profit = Rs $1,68,000$

Vedclass · Answer

(A) Let $x$ be the number of pieces of Model $A$ and $y$ be the number of pieces of Model $B$.The objective function is to maximize profit $Z = 8000x + 12000y$.The constraints based on labour hours are:$9x + 12y \leq 180 \implies 3x + 4y \leq 60$ (Fabricating)$x + 3y \leq 30$ (Finishing)$x \geq 0, y \geq 0$ (Non-negativity)The corner points of the feasible region are $O(0,0)$,$A(20,0)$,$B(12,6)$,and $C(0,10)$.Evaluating $Z$ at corner points:Corner Point$Z = 8000x + 12000y$$O(0,0)$$0$$A(20,0)$$8000(20) + 0 = 1,60,000$$B(12,6)$$8000(12) + 12000(6) = 96000 + 72000 = 1,68,000$$C(0,10)$$8000(0) + 12000(10) = 1,20,000$The maximum profit is Rs $1,68,000$ at $x=12$ and $y=6$.

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