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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.
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Solution
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
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