Question

An electric company has 300 Transistors, 400 Capacitors and 500 Inductors. The company wishes to make electronic goods using two circuits A and B. Requirement by circuit is as follows :

	Transistor	Capacitor	Inductor
A	175	300	200
B	125	100	300

The profit from circuit A and B is ₹2000 and ₹3000 respectively then constrains of the LLP based on this data are :

• A. 7x + 5y ≤ 12; 3x + y ≤ 4; 2x + 3y ≤5; x, y ≥ 0;
• B. 7x + 5y ≤ 12; x + 3y ≤ 4; 2x + 3y ≤5; x, y ≥ 0;
• C. 7x + 5y ≥ 12; 3x + y ≥ 4; 2x + 3y ≥ 5; x, y ≥ 0;
• D. 7x + 5y ≤ 12; 3x + y = 4; 2x + 3y ≤ 5; x, y ≥ 0;

Answer 1

The Correct Option is A

The problem involves determining the constraints for a Linear Programming Problem (LLP) based on the production of electronic goods using circuits A and B. We are given the available quantities of components and their requirement for each circuit. Let's identify and formulate the constraints.

Step-by-step Explanation:

1. Identify the variables:
   • Let x be the number of circuit A produced.
   • Let y be the number of circuit B produced.
2. Determine the constraints based on available components:
   • Transistor Constraint: Using the data given in the problem, we have:
     \(175x + 125y \leq 300\)
   • Capacitor Constraint:
     \(300x + 100y \leq 400\)
   • Inductor Constraint:
     \(200x + 300y \leq 500\)
3. Express the non-negativity constraints:
   • \(x, y \geq 0\)

Considering the available components and requirements, the constraints for the LLP are:

\(175x + 125y \leq 300\)
\(300x + 100y \leq 400\)
\(200x + 300y \leq 500\)
\(x, y \geq 0\)

The given options match these constraints as:

7x + 5y ≤ 12; 3x + y ≤ 4; 2x + 3y ≤5; x, y ≥ 0;

The correct answer is: 7x + 5y ≤ 12; 3x + y ≤ 4; 2x + 3y ≤5; x, y ≥ 0;