Question

Shamli wants to invest ₹ 50, 000 in saving certificates and PPF. She wants to invest atleast ₹ 15,000 in saving certificates and at least ₹ 20,000 in PPF. The rate of interest on saving certificates is 8% p.a. and that on PPF is 9% p.a. Formulation of the above problem as LPP to determine maximum yearly income, is ______.

Options

• Maximize Z = 0.08x + 0.09y

  Subject to, x + y ≤ 50,000, x ≥ 15000, y ≥ 20,000

• Maximize Z = 0.08x + 0.09y

  Subject to, x + y ≤ 50,000, x ≥ 15000, y ≤ 20,000

• Maximize Z = 0.08x + 0.09y

  Subject to, x + y ≤ 50,000, x ≤ 15000, y ≥ 20,000

• Maximize Z = 0.08x + 0.09y

  Subject to, x + y ≤ 50,000, x ≤ 15000, y ≤ 20,000

Answer 1

 

Shamli wants to invest ₹ 50, 000 in saving certificates and PPF. She wants to invest atleast ₹ 15,000 in saving certificates and at least ₹ 20,000 in PPF. The rate of interest on saving certificates is 8% p.a. and that on PPF is 9% p.a. Formulation of the above problem as LPP to determine maximum yearly income, is Maximize Z = 0.08x + 0.09y Subject to, x + y ≤ 50,000, x ≥ 15000, y ≥ 20,000.

Explanation:

Let Shamali invest ₹ x in saving certificate and ₹ y in PPF.

∴ x + y ≤ 50000, x ≥ 15000, y ≥ 20000

Total income = `8/100x + 9/100"y"`

∴ Given problem can be formulated as

Maximize Z = 0.08x + 0.09y

Subject to, x + y ≤ 50000, x ≥ 15000, y ≥ 20000.