Let x= the number of suits, y= the number of gowns.
Maximize Z=300x+500y
subject to
2x+y≤16
x+2y≤11
x+3y≤15
x≥0,y≥0
OA:x=0,0≤y≤5,Z=500y
AB:y=5−31x,0≤x≤3,Z=3400x+2500
BC:y=211−21x,3≤x≤7,Z=50x+2750
CD:y=16−2x,7≤x≤8,Z=−700x+8000
OD:y=0,0≤x≤8,Z=300x
ExtremepointO(0,0)A(0,5)B(3,4)C(7,2)D(8,0)Lines throughexreme pointx=0,y=0x=0,y=5−31xy=5−x/3,y=11/2−x/2y=11/2−x/2,y=8−2xy=8−2xy=0Objective functionvalueZ=500(0)=0Z=500(5)=2500Z=50(3)+2750=2900Z=−700(7)+8000=3100Z=300(8)=2400
The maximum value of the objective function Z=3100 occurs at the extreme point (7,2).
Hence, the optimal solution to the given LP problem is :
x=7,y=2 and maxZ=3100.
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