A company needs to develop a strategy for software product development for…
20112016
A company needs to develop a strategy for software product development for which it has a choice of two programming languages L1 and L2. The number lines of code (LOC) developed using L2 is estimated to be twice of the LOC developed with L1. The product will have to be maintained for five years. Various parameters for the company are given in the table below.
Total cost of the project includes cost of development and maintenance. What is the LOC for L1 for which of the cost of the project using L1 is equal to the cost of the project using L2?
Answer: B. 5000 — ConceptA break-even (cost-equality) problem: model each option's TOTAL cost as a function of the same unknown, then set the two totals equal and solve. Here…
- A.
4000
- B.
5000
- C.
4333
- D.
4667
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Correct answer: B
Concept
A break-even (cost-equality) problem: model each option's TOTAL cost as a function of the same unknown, then set the two totals equal and solve. Here total cost = development cost + maintenance cost. Development cost = (man-years) × (cost per man-year), and man-years = LOC / 10000. Maintenance cost = (years) × (cost per year) and is independent of LOC.
Application
Let the LOC for L1 be x. Since L2 needs twice the LOC, the LOC for L2 is 2x.
L1 development cost = (x / 10000) × 10,00,000 = 100x.
L1 maintenance cost = 5 years × 1,00,000 = 5,00,000 (fixed, no x).
Total cost (L1) = 100x + 5,00,000.
L2 development cost = (2x / 10000) × 7,50,000 = 150x.
L2 maintenance cost = 5 years × 50,000 = 2,50,000 (fixed, no x).
Total cost (L2) = 150x + 2,50,000.
Set the two totals equal: 100x + 5,00,000 = 150x + 2,50,000.
Rearrange: 5,00,000 − 2,50,000 = 150x − 100x, so 2,50,000 = 50x.
Solve: x = 2,50,000 / 50 = 5000.
Cross-check
Substitute x = 5000 back. Total (L1) = 100(5000) + 5,00,000 = 5,00,000 + 5,00,000 = 10,00,000. Total (L2) = 150(5000) + 2,50,000 = 7,50,000 + 2,50,000 = 10,00,000. Both totals are Rs. 10,00,000, so the costs match exactly at x = 5000 LOC.