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  • Two tailors, A and B, earn Rs 300 and Rs 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produc

Two tailors, A and B, earn Rs 300 and Rs 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP.

 

 

 

 
 
 
 
 

Answers (1)

Let x nad y be the number of days of which the tailors A and B work respectively
Total cost per day = Rs \left ( 300x+400y \right )
Let z denote the total cost in rupees, then z= 300x+400y
\because in one day 6 shirts are stiched by tailor A and 10 shirts are stiched By tailor B and it is denoted to produce atleast 60 shirts
\therefore 6x+10y\geq 60
It is given that 4 pairs of trousers are stiched by each tailor A and B per day to produce atleast 32 pairs of trousers
\therefore 4x+4y\geq 32
Finally the no.of shirts and pair of trousers cnanot be negative
\therefore x\geq 0,y\geq 0
Thus, mathematical formulation of the given LPP is as follows
Minimize z= 300x+400y
subject to coordinates
6x+10y\geq 60
4x+4y\geq 32
x\geq 0\; \; \, y> 0

Posted by

Ravindra Pindel

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