Question

Prabhat wants to invest the total amount of ₹15,000 in saving certificates and national saving bonds. According to rules, he has to invest at least ₹2,000 in saving certificates and ₹2,500 in national saving bonds. The interest rate is 8% on saving certificates and 10% on national saving bonds per annum. He invests \( x \) in saving certificate and \( y \) in national saving bonds. Then the objective function for this problem is:

• A. \( 0.08x + 0.10y \)
• B. \( 2000x + 2500y \)
• C. \( \frac{x}{2000} + \frac{y}{2500} \)
• D. \( \frac{x}{8} + \frac{y}{10} \)

Hint:

The objective function in a linear programming problem represents the total gain or loss.

Answer 1

The Correct Option is A

Step 1: Use the objective function formula.
The objective function represents the total interest earned from both investments. The function is given by: \[ \text{Objective Function} = 0.08x + 0.10y \] where \( x \) is the amount invested in saving certificates and \( y \) in national saving bonds.
Thus, the correct answer is (1).