A 100-pair telephone switchboard cable can utilize either enameled or tinned wire across 400 soldered joints. Soldering a joint on enameled wire costs P 1.65, whereas on tinned wire it costs P 1.15. Enameled-wire 100-pair cables cost P 0.55 per linear foot, while tinned-wire cables cost P 0.75 per linear foot. What cable run length in feet equates the installation costs for both options ?
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Answer: A. 1,000 feet
Explanation
Equating total installation costs for both wire types produces a solvable linear break even equation. Substituting joint counts and linear foot costs establishes an equality representing total project expenditure. Solving the resulting algebraic equation yields a precise break even cable run length of one thousand feet. Total installation cost equals the sum of fixed material expenses and variable joint soldering costs. Enameled wire incurs higher soldering costs but lower per foot cable costs compared to tinned wire. Break even analysis identifies the exact operational point where two competing financial alternatives become equal.
Engineers use break even cost analysis to select the most economical materials for large infrastructure projects. Telecommunication installations require careful budgeting to balance upfront cable costs against labor expenses. Minimizing total project expenditure directly improves the profitability and economic viability of engineering designs. Option B suggests one thousand forty feet which results in mismatched total installation expenditures. Option C proposes one thousand one hundred feet where the cost curves no longer intersect. Option D represents a higher foot length that fails to satisfy the financial equality condition.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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