To find: the optimal amount that should be invested in each type of investment and the optimal return..
Answer to Problem 46E
Optimal interest obtained is $27000.
Explanation of Solution
Given:
An investor has up to $450000 to invest in two types of investments. Type A pays6% annually and type B pays 10% annually. At least one half of the total portfolio is to be allocated to type A investments and at least one fourth of the portfolio is to be allocated to type B investment.
Calculation:
Consider the following objective function and their constraints. Let investment in A be considered as
Max
Fie the vertices using the above constraints.
At
At
And at the intersection of
Thus the vertices obtained are;
Plot these constraints using the vertices on a graph to find the feasible region.
Check at all these points for the maximum value of the objective function
At
At
At
Thus the optimal investment should be in half of the total for both types of investments. Their optimal interest obtained is $27000.
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
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