Optimization with economic factors.

A small electronics company is planning to expand two of its manufacturing plants. The additional annual revenue expected from the two plants is as follows:

From plant 1= 0.00002x^2 - y

From plant 2 = 0.00001y^2

Where x and y are the investments made to upgrade the facilities. Each plant requires a minimum investment of $30000.

The company can borrow a maximum of $100000 for this upgrade to be paid back in yearly installments in 10 years of an annual interest rate of 12%.

The revenue that the company generated can earn an interest at an annual interest rate of 10%. After the 10 year period, the salvage value of the upgrades is expected to be as follows;

For plant 1: 0.1x

For plant 2: 0.15y

Formulate an optimization problem to maximize the net present worth of these upgrades.

List the design variables, objective function and constraints.