Chemical Bank Is Attempting to Determine Where Its Assets Should

question 60

Essay

Chemical Bank is attempting to determine where its assets should be invested during the current year. At present, $800,000 is available for investment in bonds, home loans, auto loans, and personal loans. The annual rate of return on each type of investment is known to be the following: bonds, 12%, home loans, 18%, auto loans, 15%, personal loans, 22%. To ensure that the banks portfolio is not too risky, the bank's investment manager has placed the following restrictions on the bank portfolio:
∙ No more than 30% of the total amount invested may be in personal loans.
∙ The amount invested in home loans cannot exceed the amount invested in auto loans.
∙ The amount invested in personal loans cannot exceed the amount invested in bonds.
Determine how the bank can maximize the annual return on its investment portfolio.

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Definitions:

Sampling Distribution

The probability distribution of a statistic based on all possible samples of a fixed size from a certain population.

Sampling Distribution

The distribution of a statistic obtained by selecting all possible samples of a specific size from a population.

Mean

The mean of a collection of numbers, determined by dividing the total sum of the values by the count of the values.

Population

The entire collection of individuals or items considered for a study, from which samples are drawn for statistical analysis.