A manufacturer has 3 machines I, II and III installed in his factory. Machines I and II are capable of being operated for atmost 12 hrs whereas machine III is capable to operate 5 hrs a day. He produced only two items M and N each requiring the use of all 3 machines. Number of hours for producing 1 unit of M and N each on the 3 machines are given below:
|
Items |
No. of hours in each machine |
||
|
I |
II |
III |
|
|
M |
1 |
2 |
1 |
|
N |
2 |
1 |
1.25 |
He makes a profit of Rs. 600 on M and Rs. 400 on N. If x is the number of M items and y is the number of N items then,
A. $Z=600 x+400 y$
B. $x+2 y ≥ 12$
C. $x+\frac{5}{4} y ≤ 5$
D. $2 x+y ≤ 12$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A and C only
from question
$z=600x+400y$
constraints $(x,y≥0)$
from give hours
for machine I, II
$(1+2)x+(2+1)y≤12$
$3x+3y≤12⇒x+y≤4$
also $x+1.25y≤5⇒x+\frac{5}{4}y≤5$
So we inform that only A and C are correct