StellarCraft, a space equipment manufacturer, produces three types of space components: "Plasma Thrusters," "Navigation Systems," and "Solar Panels." StellarCraft needs to determine the optimal production plan for the next month to maximize its total profit while considering constraints on production hours and metal supply. The following data has been given to solve the problem: The company has a maximum of 3,500 hours of production time available, with each hour costing $7. The company can acquire an unlimited metal supply, but it costs $2.2 per kilogram. StellarCraft has a fixed monthly cost of $2200 associated with warehouse rent/lease. There are minimum demand requirements for each product that StellarCraft must meet. The table below presents the sale prices, the number of hours, the kilograms of metal required for each product, and the minimum demand requirements: Product Sale Price (USD) Production Hours Minimum Metal Usage (Kg) Demand Plasma Thrusters $5,000 3 hours 1.5 Kg 100 Navigation $3,000 2 hours 1.0 Kg Systems 200 Solar Panels $1,500 1.5 hours 0.8 Kg 500 Your task is to build an optimization model to estimate the optimal production schedule for the next month, considering the constraints on production hours and metal supply and ensuring that the minimum demand requirements are met for each product. The goal is to maximize the total profit (revenue minus costs), including sales revenue and the associated production and metal costs. Questions: a) (30 points) Formulate an optimization model (decision variables, objective function, and constraints) to help the company identify the optimal production plan. b) (20 points) Solve the model using Lingo/Excel and explain your results.