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 

______

Answer 1

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