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Question
Amartya wants to invest ₹ 45,000 in Indira Vikas Patra (IVP) and in Public Provident fund (PPF). He wants to invest at least ₹ 10,000 in PPF and at least ₹ 5000 in IVP. If the rate of interest on PPF is 8% per annum and that on IVP is 7% per annum. Formulate the above problem as LPP to determine maximum yearly income.
Solution: Let x be the amount (in ₹) invested in IVP and y be the amount (in ₹) invested in PPF.
x ≥ 0, y ≥ 0
As per the given condition, x + y ______ 45000
He wants to invest at least ₹ 10,000 in PPF.
∴ y ______ 10000
Amartya wants to invest at least ₹ 5000 in IVP.
∴ x ______ 5000
Total interest (Z) = ______
The formulated LPP is
Maximize Z = ______ subject to
______
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Solution
Let x be the amount (in ₹) invested in IVP and y be the amount (in ₹) invested in PPF.
x ≥ 0, y ≥ 0
As per the given condition, x + y ≤ 45000
He wants to invest at least ₹ 10,000 in PPF.
∴ y ≥ 10000
Amartya wants to invest at least ₹ 5000 in IVP.
∴ x ≥ 5000
Total interest (Z) = 0.07x + 0.08y
The formulated LPP is
Maximize Z = 0.07x + 0.08y subject to
x + y ≤ 45000
y ≥ 10000
x ≥ 5000
x ≥ 0, y ≥ 0
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