In the distant future, humanity has established colonies on multiple planets in different star systems. Interstellar trade has flourished, and Abigail Dee, an experienced entrepreneur known for her expertise in rare materials, is among the prominent traders. She operates her business from the planet Terra Nova.

Abigail specializes in sourcing and supplying rare crystals from five different planets: Aquarius, Nova Prime, Celestia, Solstice, and Stardust. Each planet possesses unique resources and demands, creating a thriving interstellar trade network. Abigail has gathered extensive data on pricing structures, shipping costs, and market demand for these crystals, enabling her to make accurate predictions.

As the current year comes to a close, Abigail is strategizing her business operations for the upcoming year. She aims to determine the optimal quantity of crystals to acquire and sell in order to maximize her profits in Galactic Credits (GC). Abigail has set several constraints and considerations based on her past experiences and market trends:

Abigail has established the following parameters:

Profitability: Abigail anticipates higher profitability in the coming year and is willing to allocate more resources accordingly.

Crystal Demand: Abigail aims to ensure a minimum sale of 100 units to each planet, requiring at least one shipment.

Limited Trips: Abigail plans to restrict the number of trips to each planet to a maximum of 5 per year.

Shipping Costs: Each trip incurs specific costs based on the distance and cargo capacity of the ships, which vary for each planet.

Resource Allocation: Abigail intends to control expenses by setting limits on resources allocated to each planet, such as fuel costs and crew size.

Market Constraints: Abigail has identified potential constraints regarding pricing, shipping, and demand for each planet.

Given these considerations, Abigail needs to determine the optimal number of crystals to acquire and sell to each planet to maximize her profits in Galactic Credits (GC). She has compiled a comprehensive chart detailing crystal pricing, exchange rates, shipping costs, crew expenses, and other relevant factors specific to each planet

given this info use solver to find the optimal solution

Crystal Pricing Shipping Costs Crystal Demand Resource Allocation Planet (GC/Unit) (GC/Trip) (Units) Limits Aquarius 250 60 100 2000 GC Nova Prime 180 70 100 1500 GC Celestia 320 80 100 3000 GC Solstice 200 90 100 2500 GC Stardust 280 100 100 3500 GC