Answer:
Let
number of rackets made = x
and
number of bats made = y
The
number of hours for making one unit of each item is given below :
Therefore
the above L.P.P. is given as
(i)
Maximize, Z = x + y, subject to the constrains
1.5x
+ 3y 3x + y
i.e. 0.5x
+ y
i.e. x
+ 2y m 3x + y
L1
: x +2y = 28 L2 : 3x + y = 24
Here
Z is maximum at E(4, 12)
Number of
Rackets = 4
Number
of Bats = 12
(ii)
Profit function is, P = 20x + 10y
Profit
is maximum at x = 4 and y = 12.
P = 20 × 4 + 10
× 12
=
80 + 120 = Rs.200.
Maximum Profit
= Rs.200.
Item
Machine time
Craftman?s time
Racket
1.5
3
Bat
3
1
Time available
42 hrs
24 hrs
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