SOLUTION: A leading firm requires software for its internal use. The firm wants to evaluate whether it is less costly to have its own programming staff and resources or to have programs dev

Question 1173650: A leading firm requires software for its internal use. The firm wants to evaluate whether it is less
costly to have its own programming staff and resources or to have programs developed by an
external development firm. The cost of both options is a function of the number of lines of code.
After the mathematical analysis, it has been estimated that the in-house development will cost $1.75
per line of code. In addition, annual overhead costs for supporting the program will be $35000.
While Software developed outside the firm costs, on average, $2.5 per line of code.
a) How many lines of code per year make the costs of the two options equal?
b) If programming needs are estimated at 35000 lines per year, what are the costs of the two
options?
c) In part b what would the in-house cost per line of code have to equal for the two options to be
equally costly?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x equal the number of lines of codes.
inside cost is 35,000 + 1.75 * x
outside cost is 2.5 * x

for the costs to be the same, 35,000 + 1.75 * x = 2.5 * x.
subtract 1.75 * x from both sides of this equation to get:
35,000 = .75 * x
solve for x to get:
x = 3,5000 / .75 = 46,666.666666...

the break even point is when x = 46,666.66666....
that's the number of lines per code per year.

2.5 * x becomes 2.5 * x = 116,666.66666... lines of code.
35000 + 1.75 * x = 116,666.66666... lines of code.

they're the same at the break even point.

if the programming needs are estimated at 35,000 lines of code per year, then the outside and inside cost would be:

outside costs = 2.5 * 35,000 = 87,500
inside costs = 5,000 + 1.75 * 35,000 = 96,250

to make the costs between inside and outside costs at 35,000 lines of code be the same, then the inside costs would have to be 87,500 as well.

this could be achieved by reducing the fixed costs or reducing the per line costs are a combination of both.

assuming the fixed cost have to remain the same, then reduction in the cost per line of code would be the only way.

let r represent the reduced cost per line of code.
the equation becomes 87,500 = 35,000 + r * 35,000
subtract 35,000 from both sides of this equation to get:|
87,500 - 35,000 = 35,000 * r
solve for r to get:
r = (87,500 - 35,000) / 35,000 = 52,500 / 35,000 = 1.5 dollars per line of code.

at that inside cost per line of code, ...

inside cost = 35,000 + 1.5 * 35,000 = 87,500
outside cost is 2.5 * 35,000 = 87,500
they're the same.

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