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A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type $B$ is at most half of that for dolls of type $A$. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of $₹ 12$ and $₹ 16$ per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?
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Let $\mathrm{x}$ dolls of type $\mathrm{A}$ and $\mathrm{y}$ dolls of type $\mathrm{B}$ are produced to have the maximum profit.
Thus L.P.P may be stated as to maximize profit, $Z=12 x+16 y$ constraints are $x+y \leq 1200, x-3 y \leq 600, y \leq \frac{x}{2}, x, y \geq 0$
$\Rightarrow \mathrm{Z}$ is maximum at $\mathrm{P}(800,400)$. The maximum value of $\mathrm{z}$ is $\mathrm{₹} 16000$.
Thus to maximize the profit 800 dolls of type A and 400 dolls of type $B$ should be produced to get a maximum profit of ₹ 16000 .
Thus L.P.P may be stated as to maximize profit, $Z=12 x+16 y$ constraints are $x+y \leq 1200, x-3 y \leq 600, y \leq \frac{x}{2}, x, y \geq 0$
$\Rightarrow \mathrm{Z}$ is maximum at $\mathrm{P}(800,400)$. The maximum value of $\mathrm{z}$ is $\mathrm{₹} 16000$.
Thus to maximize the profit 800 dolls of type A and 400 dolls of type $B$ should be produced to get a maximum profit of ₹ 16000 .
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