Deadline: $05\mathrm{.}03\mathrm{.}2024$

EcoTech Inc. is a sustainable technology company based in Istanbul, Turkey, specializing in the

production of three types of renewable energy systems: Solar Panels, Biofuel Generators, and

Hydroelectric Generators. The company's factory is equipped to manufacture these products

according to demand forecasts provided by the Sales Department for the next four months, as

detailed in Table $1$ of the case study.

At the beginning of October, EcoTech Inc. employs $24$ workers at its factory, each capable of

working $100$ hours per month during regular hours at a rate of $$30$ per hour. Additionally,

workers can work up to $50$ hours of overtime per month at a rate of $$60$ per hour. The company

has the option to hire additional workers as needed, but incurs legal costs of $$500$ per new hire,

with a monthly recruitment budget of $$5,000$ set by the Human Resources Department.

In addition to in$-$house production, EcoTech Inc. has the option to outsource a portion of the

monthly production of Biofuel Generators to a subcontractor. Any excess production beyond

monthly demand can be stored in inventory for future use, with unit inventory holding costs

calculated based on a monthly interest rate of $0\mathrm{.}4\%.$ The warehouse capacity at the factory is

limited to $500$ units for the total inventory of the three products. At the beginning of October, no

panel or generators are held in the inventory.

If a month's delivery cannot be fulfilled, backordering is permitted, allowing for late delivery of

demand with additional costs. However, all demand must be satisfied by the end of January.

For Solar Panels, Biofuel Generators, and Hydroelectric Generators, unit manufacturing costs,

unit subcontracting costs, backordering costs, and labor requirements are provided.

EcoTech Inc. aims to determine a monthly production plan for the three renewable energy

systems and a workforce plan for the four$-$month period, with the objective of minimizing total

costs. As consultants hired by the company,

a$)$ Formulate the problem as a linear programming $($LP$)$ model. Keep in mind that the model may

involve non$-$integer numbers of workers and vehicles.

b$)$ Utilize Excel Solver to solve the LP model, as the company lacks access to other optimization

packages.

c$)$ Conduct a comprehensive sensitivity analysis and compile the results into actionable

suggestions for presentation to the management of EcoTech Inc. Suggestions may include

considerations such as implementing a salary increase in January or negotiating terms with

subcontractors to optimize costs and improve efficiency.

$($pls write the LP model in both extended and algebraic form, show clearly the steps of how to solve this problem in excel solver$)$