GATE CS 2011 Q.5 (CS Q.5): Asymptotic Analysis and Time/Space Complexity

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 of lines of code (LOC) developed using L2 is estimated to be twice 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.

Parameter	Language L1	Language L2
Man years needed for development	LOC / 10000	LOC / 10000
Development Cost per man year	Rs 10,00,000	Rs 7,50,000
Maintenance time	5 years	5 years
Cost of maintenance per year	Rs 1,00,000	Rs 50,000

Total cost of the project includes cost of development and maintenance. What is the LOC for L1 for which the cost of the project using L1 is equal to the cost of the project using L2?

4000

5000

4333

4667

Official answer and solution

Official answer: B
From: Official GATE 2011 answer key

Solution

Formulate total project cost equations for both languages as functions of LOC and solve for the break-even point.

Let the lines of code developed using language L1 be $L$ . Then the lines of code developed using L2 is $2L$ .

For language L1:

Development effort = $\frac{L}{10000}$ man-years.
Development cost = $\frac{L}{10000} \times 10,00,000 = 100 L$ .
Maintenance cost over 5 years = $5 \times 1,00,000 = 5,00,000$ .
Total cost for L1 = $100 L + 500000$ .

For language L2:

Development effort = $\frac{2L}{10000}$ man-years.
Development cost = $\frac{2L}{10000} \times 7,50,000 = 150 L$ .
Maintenance cost over 5 years = $5 \times 50,000 = 2,50,000$ .
Total cost for L2 = $150 L + 250000$ .

Equating total costs:

100 L + 500000 = 150 L + 250000 \implies 50 L = 250000 \implies L = 5000

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2011 Computer Science and Information Technology (CS)
Question: 5 of 65, printed as CS Q.5
Section: Computer Science and Information Technology

This question is from a part of the syllabus that is no longer in GATE CS. It is kept because it was in the paper.

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