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Home » A small firm manufactures gold rings and chains. The combined number of rings and chains manufactured per day is at most 24. It takes 1 hour to make a ring and half an hour for a chain. The maximum number of hour to available per day is 16 . If the profit on a ring is 300 and that on a chain is 190, how many of each should be manufactured daily so as to maximize the profit?
A small firm manufactures gold rings and chains. The combined number of rings and chains manufactured per day is at most 24. It takes 1 hour to make a ring and half an hour for a chain. The maximum number of hour to available per day is 16 . If the profit on a ring is 300 and that on a chain is 190, how many of each should be manufactured daily so as to maximize the profit?
CBSE | Class 12 | Exercise 33B | Linear Programming | Maths | RS Aggarwal
A small firm manufactures gold rings and chains. The combined number of rings and chains manufactured per day is at most 24. It takes 1 hour to make a ring and half an hour for a chain. The maximum number of hour to available per day is 16 . If the profit on a ring is 300 and that on a chain is 190, how many of each should be manufactured daily so as to maximize the profit?

Let x and y be number of gold rings and chains.
\therefore According to the question,
x+y \leq 24, x+0.5 y \leq 16, x \geq 0, y \geq 0
Maximize Z=300 x+190 y
The feasible region determined by x+y \leq 24, x+0.5 y \leq 16, x \geq 0, y \geq 0 is given by

The corner points of feasible region are A(0,0), B(0,24), C(8,16), D(16,0). The value of Z at corner points are

    \[\begin{tabular}{|l|l|l|} \hline Corner Point & $\mathrm{Z}=300 \mathrm{x}+190 \mathrm{y}$ & \\ \hline $\mathrm{A}(0,0)$ & 0 & \\ \hline $\mathrm{B}(0,24)$ & 4560 & \\ \hline $\mathrm{C}(8,16)$ & 5440 & \\ \hline $\mathrm{D}(16,0)$ & 4800 & \\ \hline \end{tabular}\]

The maximum value of Z is 5440 at point (8,16).
Hence, the firm should manufacture 8 gold rings and 16 gold chains to maximize their profit.

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