A small business enterprise makes dresses and trousers. To make a dress
requires 1
2
hour of cutting and 20 minutes of stitching. To make a trouser
requires 15 minutes of cutting and 1
2
hours of stitching. The profit on a dress is
P40 and on a pair of trousers is P50. The business operates for a maximum of
8 hours per day. Determine how many dresses and trousers should be made to
maximize profit and what the maximum profit is.
Let x,y- number of dresses and trousers to done.
Mathematical model is
z=40 x+25 y max;
50 x+45 y 480
(or 10 x+9 y 96)
x,y 0
x,y Z
Because x is integer
1) x=9,
2) x=8,y=
3) x=7,y=
4) x=6,y=
5) x=5,y=
6) x=4,y=
7) x=3,y=
cases x=0,1,2 worse than dest case (x=10) because 2
Now all possibilities are considered and optimal solution (xopt,yopt)=(10,0) with zopt=360.
So xopt=10,yopt=0,zopt=360.
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