A manufacturer of electronic circuit has a stock of 200 resistors, 120 transistors and 150 capacitors and is required to produce two types of circuits A and B. Type A requires 20 resistors, 10 transistors and 10 capacitors. Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type A circuit is ₹50 and that on type B circuit is ₹60, identify the constraints for this LPP, if it was assumed that x circuit B of type A and y circuits of type B was produced by the manufacturer.
A. x +2y ≥ 15
B. 2x + y ≤ 20
C. x + 2y ≤ 12
D. x , y ≤ 0
Choose the correct answer from the options given below
Answer & explanation
Correct answer: option 2
Let the manufacture produces x units of type A circuits and y units of type B circuits. From the given information, we have following corresponding constraint table:
|
|
Type A (x) |
Type B (y) |
Maximum stock |
|
Resistors |
20 |
10 |
200 |
|
Transistors |
10 |
20 |
120 |
|
Capacitors |
10 |
30 |
150 |
|
Profit |
Rs 50 |
Rs 60 |
|
Total profit Z = 50x + 60y (in ₹)
Now, we have following mathematical model for the given problem
Maximize, Z: \(50x + 60y ----(i)\)
Subject to the constraints.
20x + 10y ≤ 200 [resistors constraint]
⇒ 2x + y ≤ 20 .........(ii)
and 10x + 20y ≤ 120 [transistor constraint]
⇒ x + 2y ≤ 12 ........(iii)
and 10x + 30y ≤ 150 [capacitor constraint]
⇒ x + 3y ≤ 15.......(iv)
x ≥ 0, y ≥ 0 [non-negative constraint].
So, the maximum, Z\( =50x + 60y\), subject to \(2x + y ≤ 20,\, \ x + 2y ≤ 12, \, \ x + 3y ≤ 15,\, \ x ≥ 0, y ≥ 0\)