A factory needs a minimum of 1200 tons of raw material and at least 100 workers to start its production. There are three suppliers each agreed to supply 600, 800 and 1250 tons of raw materials respectively.
A=1 if the first supplier supplies else it is 0.
B=1 if the second supplier supplies else it is 0.
C=1 if the third supplier supplies else it is 0.
D=1 if 100 workers are available else it is 0.
R=1 if production starts else it is 0.
(a) Taking A, B, C and D as inputs and R as output draw truth table for the problem stated above and derive its SOP expression.
(b) Reduce the above SOP expression using the K-map.

SOP expression:
A'B'CD + A'BCD + AB'CD + ABC'D + ABCD

K-Map to reduce the expression:

From Quad (3,7,15,11):
Rows representing the Quad: 1 (Both variables A and B are in opposite form. Hence, they get cancelled.)
Columns representing the Quad: CD
Term Obtained = CD

From Pair (13,15):
Rows representing the Pair: AB
Columns representing the Pair: C'D + CD = D
Term Obtained = ABD

Result = ABD + CD