Question

A shopkeeper wants to purchase two articles A and B of cost price \( 4 \) and \( 3 \) respectively. He thought that he may earn 30 paise by selling article A and 10 paise by selling article B. He has not to purchase total articles worth more than \( 24 \). If he purchases the number of articles of A and B, \( x \) and \( y \) respectively, then linear constraints are

• A. \( x \geq 0, y \geq 0, 4x + 3y \leq 24 \)
• B. \( x \geq 0, y \geq 0, 3x + 10y \leq 24 \)
• C. \( x \geq 0, y \geq 0, 4x + 3y \leq 24 \)
• D. \( x \geq 0, y \geq 0, 30x + 40y \geq 24 \)

Hint:

For linear programming problems, define the constraints based on the given limitations on resources and profits.

Answer 1

The Correct Option is C

Step 1: Define the constraints.
The constraints on the number of articles are based on the total cost and the earnings. The inequality \( 4x + 3y \leq 24 \) ensures that the total cost does not exceed the limit.
Step 2: Conclusion.
The linear constraints are \( x \geq 0, y \geq 0, 4x + 3y \leq 24 \). Final Answer: \[ \boxed{x \geq 0, y \geq 0, 4x + 3y \leq 24} \]