Q. 114.5( 2 Votes )

A small firm manu

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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