Answer :

Let number of necklaces manufactured be x and y be the number of bracelets manufactured.

As the total number of items are at most 24;

∴ x + y ≤ 24 ……(i)

Necklaces takes half an hour and Bracelets takes 1 hour to manufacture.

⇒ x items take x/2 hours and y items take y hours to manufacture and the total time available is 16 hours.

∴ x + 2y ≤ 32 ……(ii)

The profit of one necklace is Rs. 100 and that of bracelet is Rs. 300.

Let the profit be Z

∴ Z = 100x + 300y ……(iii)

Equations (i), (ii) and (iii) forms the LPP.

(0,0),(0,16),(16,8) and (24,0) are the boundary points.

At (0,0) Z = 0

At (0,16) Z = 4800

At (16,8) Z = 4000

At (24,0) Z = 2400

Since at least one of each should be produced;

16 necklaces and 8 bracelets should be produced daily for maximum profit.

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