Optimal Lending

question 26

Essay

Optimal Lending. Penny Lane is a senior loan officer with Citrus National Bank in Tampa, Florida. Lane has both corporate and personal lending customers. On average, the profit contribution margin or interest rate spread is 1.75% on corporate loans and 2.25% on personal loans. This return difference reflects the fact that personal loans tend to be riskier than corporate loans. Lane seeks to maximize the total dollar profit contribution earned, subject to a variety of restrictions on her lending practices. In order to limit default risk, Lane must restrict personal loans to no more than 40% of total loans outstanding. Similarly, to ensure adequate diversification against business cycle risk, corporate lending cannot exceed 80% of loaned funds. To maintain good customer relations by serving the basic needs of the local business community, Lane has decided to extend at least 40% of her total credit authorization to corporate customers on an ongoing basis. Finally, Lane cannot exceed her current total credit authorization of $50 million.
A. Using the inequality form of the constraint conditions, set up and interpret the linear programming problem Lane would use to determine the optimal dollar amount of credit to extend to corporate (C) and personal (P) lending customers. Also formulate the LP problem using the equality form of the constraint conditions.
B. Use a graph to determine the optimal solution, and check your solution algebraically. Fully interpret solution values.

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Definitions:

Nominal GDP

Nominal GDP is the market value of all final goods and services produced within a country in a given period, measured in current prices.

Aggregate Output

The total value of all goods and services produced in an economy over a specific time period.

Aggregate Supply

The total supply of goods and services that firms in an economy plan on selling during a specific time period at given prices.

Price Level

A measure of the average prices of goods and services in an economy at a given time.