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Home » A manufacture makes two product, A and B. product A sells at each and takes hour to make. Product B sells at each and takes 1 hour to make. There is a permanent order for 14 of product and 16 of product B. A working week consist of 40 hours of production and the weekly turnover must not be less than \mp10000. If the profit on each of the product is and on product , it is then how many of each should be produced so that the profit is maximum? Also, find the maximum profit.
A manufacture makes two product, A and B. product A sells at \mp 200 each and takes \frac{1}{2} hour to make. Product B sells at \{300 each and takes 1 hour to make. There is a permanent order for 14 of product A and 16 of product B. A working week consist of 40 hours of production and the weekly turnover must not be less than \mp10000. If the profit on each of the product A is \mp 20 and on product B, it is \mp 30 then how many of each should be produced so that the profit is maximum? Also, find the maximum profit.
CBSE | Class 12 | Exercise 33B | Linear Programming | Maths | RS Aggarwal
A manufacture makes two product, A and B. product A sells at \mp 200 each and takes \frac{1}{2} hour to make. Product B sells at \{300 each and takes 1 hour to make. There is a permanent order for 14 of product A and 16 of product B. A working week consist of 40 hours of production and the weekly turnover must not be less than \mp10000. If the profit on each of the product A is \mp 20 and on product B, it is \mp 30 then how many of each should be produced so that the profit is maximum? Also, find the maximum profit.

Let x and y be number of A and B products.
\therefore According to the question.
0.5 x+y \leq 40,200 x+300 y \geq 10000, x \geq 14, y \geq 16
Maximize Z=20 x+30 y
The feasible region determined by 0.5 x+y \leq 40,200 x+300 y \geq 10000, x \geq 14, y \geq 16 is given by

The corner points of feasible region are A(14,33), B(14,24), C(26,16), D(48,16).The value of Z at corner points are

    \[\begin{tabular}{|l|l|l|} \hline Corner Point & $\mathrm{Z}=20 \mathrm{x}+30 \mathrm{y}$ & \\ \hline $\mathrm{A}(14,33)$ & 1270 & \\ \hline $\mathrm{B}(14,24)$ & 1000 & \\ \hline $\mathrm{C}(26,16)$ & 1000 & \\ \hline $\mathrm{D}(48,16)$ & 1440 & \\ \hline \end{tabular}\]

The maximum value of Z is 1440 at point (48,16).
Hence, the manufacturer should manufacture 48 A products and 16 \mathrm{~B} products to maximize their profit of Rs. 1440 .

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