A retired person has 70000 to invest and two types of bonds are available in the market for investment. First type of bond yields an annual income of 8% on the amount invested and the second type of bond yields 10% per annum. As per norms, he has to invest minimum of 10000 in the first type and not more than 30000 in the second type. How should he plan his investment, so as to get maximum return after one year of investment. Make it an L.P.P. and solve the above problem.
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Answer:
Step-by-step explanation:
A retired person has 70000 to invest and two types of bonds are available in the market for investment. First type of bond yields an annual income of 8% on the amount invested and the second type of bond yields 10% per annum. As per norms, he has to invest minimum of 10000 in the first type and not more than 30000 in the second type. How should he plan his investment, so as to get maximum return after one year of investment.
So let us take as I case and II case:
I case: When profit is 8%, investment is greater than or equal to 10,000
II case: When profit is 10%, investment is less than or equal to 30,000
Let p and q be the investment in first and second type of bonds.
So R = 8% of p + 10% of q
So p + q ≤ 70,000
p ≥ 10,000
q ≤ 30,000
hence maximum profit will be 8% of p + 10% of q = 8p / 100 + 10q/100