Question

Lazer Technologies Inc. (LTI) 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

UNIT NUMBER		COST ($ MILLIONS)			UNIT NUMBER	COST ($ MILLIONS)
1		$	13.0		11	$	3.7
2			8.8		12		3.6
3			7.4		13		3.4
4			6.2		14		3.4
5			5.7		15		3.2
6			5.2		16		3.2
7			4.8		17		3.0
8			4.5		18		2.9
9			4.2		19		2.8
10			4.0		20		2.8

a. Based on past experience, what is the learning rate? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

b. What bid should LTI submit for the total order of 100 units, assuming that learning continues?

c. What is the cost expected to be for the last unit under the learning rate you estimated?

Answer 1

Learning curve demonstrates connection between unit generation time and the aggregate number of unit created and is portrayed by a line it has immense appropriateness in the field of business and assembling by the method for evaluating the ideal opportunity for the item structure generation and costs it is additionally utilized for arranging corporate methodology viz. evaluating choice capital investment and assurance of operating costs.

learning curve rate should be evaluated by ascertaining the normal expectation to absorb learning curve with each multiplying of creation the expectation to learn and adapt rate is determined by separating the estimation of the succeeding unit by the benefit of preceding unit as far as time or cost

a.

Calculation of learning rate for 20 high power laser systems being produced by LTI :

From the above given table we have the unit numbers 1 to 5 = 5.7/13 = 43.84 %

unit numbers 5 to 10 = 4.0/5.7 = 70.175%

unit numbers 10 to 15 = 3.2/4.0 = 80%

unit numbers 15 to 20 = 2.8/3.2 = 87.5%

Learning Rate = (43.84+70.175+80+87.5) / 4 = 70.37%

So the obtained value of LEARNING RATE is = 70.37%

b. The Average cost of 100 units can be estimated by using exhibit 6.4 and 6.5 cumulative improvement factors

The cumulative improvement factor for 100th unit at 70.37% learning rate is 0.0935 ( using exhibit 6.4)

The cumulative improvement factor for 100th unit at 70.37% learning rate is 17.79 ( using exhibit

6.5)

for 120th unit at 70.37% learning rate is 19.57 ( using 6.5 exhibit)

for 120th unit at 70.37% learning rate is 0.0851 ( using 6.4 exhibit)

estimated cost to produce 120 units is $13M x 19.57 =$254.41M (by using 6.5 exhibit)

estimated cost to produce 120 units is $13M x 0.0851 =$11.063M (by using 6.4 exhibit)

The cumulative improvement factor for the 20th unit at 70.37% learning is 7.407 (by using 6.5 exhibit) = $13M x 7.407 = $96.291M

The cumulative improvement factor for the 20th unit at 70.37% learning is 0.2141 (by using 6.4 exhibit) =$13M x 0.2141 = $2.7833M

so there fore for cost of 100 units = cost of 120 units -cost of 20 units

cost of 100 units = $254.41M-$96.291M

cost of 100 units = $158.12M ( by using 6.5 exhibit table )

so there fore for cost of 100 units = cost of 120 units -cost of 20 units

cost of 100 units = $11.063M-$2.7833M

cost of 100 units = $8.2797M ( by using 6.4 exhibit table )

c. estimate the cost of producing 120 th unit

Note : estimated cost to produce 120 units is $13M x 0.0851 =$1.1063M (by using 6.4 exhibit)

so we conclude that here expected for the last unit under 70.37% learning rate is $1.1063M