Question

Shraddho wants to invest at most ₹ 25,000/- in saving certificates and fixed deposits. She wants to invest at least ₹ 10,000/- in saving certificate and at least ₹ 15,000/- in fixed deposits. The rate of interest on saving certificate is 5% and that on fixed deposits is 7% per annum. Formulate the above problem as LPP to determine maximum income yearly.

Answer 1

Let x₁: amount (in ₹) invest in saving certificates.

x₂: amount (in ₹) invest in fixed deposits, x₁ x₂ ≥ 0.

From given conditions, x₁ + x₂ ≤ 25,000

Also, Shraddha wants to invest at least ₹ 10,000/- in saving certificate.

∴ x₁ ≥ 10,000

Also, She wants to invest at least ₹ 15,000/- in fixed deposits.

∴ x₂ ≥ 15,000

Total interest = z = 0.05x₁ + 0.07x₂

Maximize z = 0.05x₁ + 0.07x₂  subject to

x₁ + x₂ ≤ 25,000

x₁ ≥ 10,000

x₂ ≥ 15,000

x₁, x₂ ≥ 0