A ship captain who buys commodities on islands where they are cheap and selling them on islands where they cost more. For this, he uses a fleet of ships that can cargo (tradeable commodities) and shield themselves and the rest of your fleet from thieves. Ships are reviewed by their tons of cargo that they can carry and their "Combat Rating," this is the number of tons they can protect from being marauded by pirates, and the number of operating crew. There are 2 ships that can be purchase: Name Corvette Freighter Cargo Combat 10T 0 100T 0. ShipCost Crew $1M $10M 1 10 So, it would take 10 Corvettes to fully protect the cargo of one freighter. If any cargo is left unprotected there is a 50% chance that it will be raided by pirates and taken.
A ship captain who buys commodities on islands where they are cheap and selling them on islands where they cost more. For this, he uses a fleet of ships that can cargo (tradeable commodities) and shield themselves and the rest of your fleet from thieves. Ships are reviewed by their tons of cargo that they can carry and their "Combat Rating," this is the number of tons they can protect from being marauded by pirates, and the number of operating crew. There are 2 ships that can be purchase: Name Corvette Freighter Cargo Combat 10T 0 100T 0. ShipCost Crew $1M $10M 1 10 So, it would take 10 Corvettes to fully protect the cargo of one freighter. If any cargo is left unprotected there is a 50% chance that it will be raided by pirates and taken.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:**Title: Efficient Fleet Management and Risk Assessment for Maritime Trade**
**Introduction:**
A ship captain engages in trading by purchasing commodities on islands where they are inexpensive and selling them on islands where prices are higher. The captain uses a fleet of ships capable of carrying cargo and shielding themselves and other fleet members from theft.
**Fleet Options:**
1. **Corvette**
- **Cargo Capacity:** 0 tons
- **Combat Rating:** 10 tons
- **Cost:** $1M
- **Crew Required:** 1
2. **Freighter**
- **Cargo Capacity:** 100 tons
- **Combat Rating:** 0 tons
- **Cost:** $10M
- **Crew Required:** 10
A ship's "Combat Rating" specifies the tonnage it can protect from pirate raids.
**Protection and Risk Assessment:**
- Ten Corvettes are required to fully protect one Freighter’s cargo.
- If cargo is left unprotected, there is a 50% risk of being raided.
**Economic Scenario:**
- **Daily Operations:** Purchase food at $500/ton, sell for $725/ton.
- **Crew Costs:** $1,000 per crew member daily.
- **Budget:** $100M with a 1.75% annual interest rate on savings.
**Tasks:**
1. **Profit Maximization with Partial Protection:**
- Determine if allowing some unprotected cargo increases profits.
- Formulate an expression for expected profits when using fewer than 10 Corvettes per Freighter.
2. **Comparison of Fleet Configurations:**
- Calculate the profitability of maximum Corvette purchase versus no Corvettes for each Freighter.
- Assess if spending the entire $100M on ships yields equal profits in both configurations.
This analysis will help optimize ship and resource allocation, understanding the balance between risk and profit in maritime trade.
Expert Solution
Step 1
As per given information
There are 2 types of ships in the fleet.
Corvette and Freighter
Corvette has the capacity to protect 10T from stealing by Pirates.
The freighter has the capacity to shield 100 T from thieves.
Cost of 1 Corvette $1M and it requires to 1 crew
Cost of 1 freighter $10M and it requires to 10 crew
Buying food price=$500 per ton and selling price=$725 per ton
Cost of the per crew member =$1000 per day
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