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.