Question

9. The government agency for which a con- tractor has been working has notified the contractor of a desire to extend the origi- al contract to include three additional units. The initial contract called for four units to be built and delivered. The con- tractor must now estimate the total time required to complete the next three units. Upon reviewing records for the original contract, it was discovered that data for the second unit are inaccurate and cannot be used. It is known that the årst unit re quired 16 days, the third 12.5 days, and the fourth 11.5 days. Determine an estimated time for the next three units.

Answer 1

Given, t1 = 16 days

Let t2 be x

Unit	Unit Time	Cumulative Time
t1	16	16
t2	x	16+x
t3	12.5	16+x+12.5 = 28.5 + x
t4	11.5	28.5+x+11.5 = 40 + x

t₄= t₁ * n^b = 16 * (4)^(b) = (40+x)

t₃= t₁ * n^b = 16 * (3)^(b) = (28.5+x)

Evaluate t₄ - t₃ => 16((4^b)-(3^b)) = 11.5

((4^b)-(3^b)) = 11.5/16 = 0.718

Taking log on both sides:

b log 4 – b log 3 = log 0.718 = -0.144

b( log 4 – log 3) = -0.144

b(log(4/3)) = -0.144

b(log 1.333) = -0.144

b* 0.125 = -0.144

Or b = -0.144/0.125 = -1.152

b= log learning rate / log 2

-1.152 = log learning rate / log 2

log learning rate = -1.152 * log 2 = -1.152 * 0.301 = -0.3467

learning rate = antilog (-0.3467) = 0.45 = 45%

Time for learning the next 3 units:

t₅= t₁ * n^b = 16 * (5^(-1.152)) = 2.505 days

t₆= t₁ * n^b = 16 * (6^(-1.152)) = 2.030 days

t₇= t₁ * n^b = 16 * (7^(-1.152)) = 1.7 days