Question 1163384: Part A
A leading firm requires a 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 are 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 codes per year make 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 be the in-house cost per line of code have to equal for the two options to be equally costly?
Part B
Because the parameters used in mathematical models are frequently estimates, actual results may differ from those projected by the aforementioned mathematical analysis. To account for some of the uncertainities which may exist in a problem, analysts often conduct sensitivity analysis. The objective is to assess how much a solution might change if there are changes in model parameters. Assume in part A that the software development costs by outside firms might actually fluctuate by ±15%.
Compute the breakeven points if the costs are 15 percent higher or lower and compare your results with the mathematical model achieved prior to the sensitivity analysis.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! in house development costs are modeled by the equation:
c = 35,000 + 1.75 * x
c is the cost
x is the number of lines of code.
35,000 is the overhead cost.
this cost remains the same regardless of how many lines of cost are developed (not totally true, but within a specified range, it would apply).
software developed out of house equals 2.50 per line of code.
the equation for that would be:
c = 2.5 * x
your questions are:
part A question a) How many lines of codes per year make costs of the two options equal?
part A question b) If programming needs are estimated at 35000 lines per year, what are the costs of the two options?
part A question c) In part b what would be the in-house cost per line of code have to equal for the two options to be equally costly?
part B question 1) Assume in part A that the software development costs by outside firms might actually fluctuate by ±15%.
Compute the breakeven points if the costs are 15 percent higher or lower and compare your results with the mathematical model achieved prior to the sensitivity analysis.
part A question a) How many lines of codes per year make costs of the two options equal?
if the cost are to be equal, then 35,000 + 1.75 * x = 2.50 * x.
subtract 1.75 * x from both sides of the equation to get:
35,000 * x = .75 * x
solve for x to get:
x = 35,000 / .75 = 46,666.66666.....
when that number of lines of code are developed:
the in house cost are 35,000 + 1.75 * 46,666.66666..... = 116,666.66666...
the out of house coss are 2.50 * A = 116,666.66666.....
they're the same.
part A question b) If programming needs are estimated at 35000 lines per year, what are the costs of the two options?
in house costs will be 35,000 + 1.75 * 35,000 = 96,250
out of house costs will be 2.50 * 35,000 = 87,500
part A question c) In part b what would be the in-house cost per line of code have to equal for the two options to be equally costly?
let a equal the cost per line of code for the in house estimate.
the equation for in house becomes c = 35,000 + a * x
the equation for out of house stays the same.
out of house cost = 2.5 * 35,000 = 87,500
in house cost equation of c = 35,000 + a * x becomes:
87,500 = 35,000 + a * 35,000
subtract 35,000 from both sides of this equation to get:
87,500 - 35,000 = a * 35,000
combine like terms to get:
52,500 = a * 35,000
solve for a to get:
a = 52,500 / 35,000 = 1.5
the in house variable cost per line of code would have to be 1.5.
you would then get:
in house cost = 35,000 + 1.5 * 35,000 = 87,500
part B question 1) Assume in part A that the software development costs by outside firms might actually fluctuate by ±15%.
Compute the breakeven points if the costs are 15 percent higher or lower and compare your results with the mathematical model achieved prior to the sensitivity analysis.
the software development costs for out of house are estimated to be 2.50.
if the costs were 15% higher, then the costs would be equal to 1.15 * 2.50 = 2.875.
if the costs were 15% lower, than the costs would be equal to .85 * 2.50 = 2.125.
the costs for out of house developments becomes:
normal estimate = 2.5 * x.
15% higher estimate = 2.875 * x.
15% lower estimate = 2.125 * x.
the in house development cost remains at 35,000 + 1.75 * x
for normal estimate break even analysis, you get:
2.5 * x = 35,000 * 1.75 * x
subtract 1.75 * x from both sides of the equation to get:
2.5 * x - 1.75 * x = 35,000
combine like terms to get:
.75 * x = 35,000
solve for x to get x = 35,000 / .75 = 46,666.66666.....
for high estimate break even analysis, you get:
2.875 * x = 35,000 * 1.75 * x
subtract 1.75 * x from both sides of the equation to get:
2.875 * x - 1.75 * x = 35,000
combine like terms to get:
1.125 * x = 35,000
solve for x to get:
x = 35,000 / 1.125 = 31,111.11111.....
for low estimate break even analysis, you get:
2.125 * x = 35,000 + 1.75 * x
subtract 1.75 * x from both sides of the equation to get:
2.125 * x - 1.75 * x = 35,000
combine like terms to get:
.375 * x = 35,000
solve for x to get:
x = 35,000 / .375 = 93,333.33333.....
your break even analysis results are:
at normal out of house costs, the break even point is at 46,666.66666..... lines of code.
at 15% higher out of house costs, the break even point is at 31,111.11111..... lines of code.
at 15% lower out of house costs, the break even point is at 93,333.33333..... lines of code.
these equations can be placed on a graph as shown below:
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