The distance covered by the underwater cable is equal to x miles. Laying 3 miles of cable underground in scenario 1 is more economical than laying 4 miles underground in scenario 2. It is unlikely that your boss would fire you based on this decision.
Cost Analysis for Telephone Cable Project
Scenario 1: 3 miles underground + underwater cable
Distance from the terminal box to the island: unknown
Distance covered by underground cable: 3 miles
Cost of underground cable: $500/mile * 3 miles = $1500
Distance covered by underwater cable: unknown
Cost of underwater cable: $1100/mile * unknown distance
To calculate the total cost, we need the distance covered by the underwater cable.
Let x be the distance from the island to the point where the underground cable ends (3 miles from the terminal box).
Using the Pythagorean theorem:
(Distance from terminal box to island)^2 = (3 miles)^2 + (x miles)^2
Distance from terminal box to island = √((3 miles)^2 + (x miles)^2)
To minimize the cost, we need to find the shortest distance for the underwater cable.
The shortest distance will occur when the underwater cable goes straight from the island to the point where the underground cable ends, forming a right triangle.
Therefore, the distance covered by the underwater cable is equal to x miles.
Calculating the total cost:
Total cost = $1500 + $1100/mile * x miles
Total cost = 1500 + 1100x
Scenario 2: 4 miles underground + underwater cable
Distance covered by underground cable: 4 miles
Cost of underground cable: $500/mile * 4 miles = $2000
Distance covered by underwater cable: unknown
Cost of underwater cable: $1100/mile * unknown distance
Following the same logic as scenario 1:
Distance from terminal box to island = √((4 miles)^2 + (x miles)^2)
Total cost = $2000 + $1100/mile * x miles
Total cost = 2000 + 1100x
Comparing the costs:
To determine which scenario is more economical, we need to compare the total costs of both scenarios.
Scenario 1: 1500 + 1100x
Scenario 2: 2000 + 1100x
Since the cost of the underwater cable is the same in both scenarios, the scenario with the lower cost for underground cable will be more economical.
Comparing the cost of underground cable:
Scenario 1: $1500
Scenario 2: $2000
Therefore, laying 3 miles of cable underground in scenario 1 is more economical than laying 4 miles underground in scenario 2.
Job Security:
Based on the analysis, your proposal for laying 3 miles of cable underground is more economical than your boss's proposal. This demonstrates your ability to analyze data and make sound decisions, which is a valuable asset for any engineer.
Therefore, it is unlikely that your boss would fire you based on this decision. However, it is always important to be open to feedback and consider alternative solutions, as your boss might have additional information or perspectives that could further optimize the project.
Conclusion:
Laying 3 miles of cable underground before starting the underwater cable is the more economical option for this project. Your analysis demonstrates your ability to solve problems effectively, which is likely to ensure your job security.