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Question
Mr. Anil wants to invest at most Rs. 60,000 in Fixed Deposit (F.D.) and Public Provident Fund ( P.P.F. ). He wants to invest at least Rs. 20,000 in F.D. and at least Rs. 15,000 in P.P.F. The rate of interest on F.D. is 8% p.a. and that on P.P.F. is 10% p.a. Formulate the above problem as L.P.P. to determine maximum yearly income.
Solution
Let Rs. x thousand and Rs. y thousand be invested in Fixed Deposit (F.D.) and Public Provident Fund (P.P.F.) respectively.
∴ x ≥ 0, y ≥ 0
As amount to be invested is at most< Rs. 60,000
∴ x + y ≤ 60,000
As he wants to invest at least Rs. 20,000 in FD and at least Rs. 15,000 in PPF.
∴ x ≥ 20,000 and y ≥ 15,000
Let total yearly income be Rs. 'Z'
∴ z = ( 8% of x ) + (10% of y )
z = `8/100x + 10/100y`
z = 0.08x + 0.1y
Hence L.P.P. is
Maximize : z = 0.08x + 0.1y
Subject to x + y ≤ 60,000
x ≥ 20,000 and y ≥ 15,000
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