Lazer Technologies Inc. (LIT) has produced a total of 20 high-power laser system
ID: 343251 • Letter: L
Question
Lazer Technologies Inc. (LIT) has produced a total of 20 high-power laser systems that could be used to destroy any approaching enemy missiles or aircraft. The 20 units have been produced, funded in part as private research within the research and development arm of LTI, but the bulk of the funding came from a contract with the U.S. Department of Defense (DoD) Testing of the laser units has shown that they are effective defense weapons, and through redesign to add portability and easier field maintenance, the units could be truck mounted DoD has asked LTI to submit a bid for 100 units The 20 units that LTI has built so far cost the following amounts and are listed in the order in which they were produced: Use Exhibit 6.4 and Exhibit 6.5 NUMBER ( MILLIONS) NUMBER (S MILLIONS) $12.0 10.6 $8.3 8.3 8.1 8.0 10.2 9.5 9.4 9.2 8.9 8.7 8.6 8.5 12 13 14 15 16 17 18 19 20 7.8 7.7 7.6 7.7 10 a. Based on past experience, what is the learning rate? (Do not round intermediate calculations. Round your answer to the nearest whole percent.) Learning rate 96 b. What bid should LTI submit for the total order of 100 units, assuming that learning continues? Cost for 100 more units S c. What is the cost expected to be for the last unit under the learning rate you estimated? Expected cost for last unitExplanation / Answer
Learning rate ( expressed in fraction terms ) is such that when quantity doubles, cost/ time to produce the last unit becomes = Learning rate x Cost/ time to produce first unit
For example if learning rate ( in fraction terms ) is r and ,
If cost to produce first unit = $12
Cost to produce 2nd unit = r x $12
Cost to produce 4th unit = r^2 x $12
Cost to produce 8th unit = r^3 x $12
Cost to produce 16th unit = r^4 x $12
It is given that cost of 16th unit = $ 7.8 million
Therefore ,
7.8 = r^4 x 12
Or, r^4 = 7.8/12
Or, r^4 = 0.65
Or, r = ( 0.65)^(1/4)
Or, r = 0.8979 ( or, 89.79 % or 90% rounded to nearest whole number )
LEARNING RATE = 90%
To calculate ,
Total bid value of additional 100 units , one must calculate :
To calculate both of the above , we will consider following :
Cost of first unit = $12
Learning rate = 90%
We will use standard Learning curve table to derive above values .
Using above data and learning curve table :
Total cost of 120 items = $815.11
Total cost of first 20 items = $175.29
Therefore, bid value of additional 100 units
= Total cost of 120 items – Total cost of first 20 items
= $815.11 - $175.29
= $639.82
Expected cost of the last unit i.e. 120th unit as derived basis learning curve table = $5.8
COST FOR 100 MORE UNITS = $639.82
EXPECTED COST FOR THE LAST UNIT = $5.8
LEARNING RATE = 90%
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