A start-up firm has kept careful records of the time required to manufacture itsproduct, a shutoff valve used in gasoline pipelines.Cumulative Number Number of Hours Requiredof Units Produced for Next Unit50 3.3100 2.2400 1.0600 0.81,000 0.510,000 0.2a. Compute the logarithms of the numbers in each column. (Use natural logs.)b. Graph the ln(hours) against the ln(cumulative units) and eyeball a straight-linefit of the data. Using your approximate fit, estimate a and b.c. Using the results of part (b), estimate the time required to produce the first unitand the appropriate percentage learning curve that fits these data.d. Repeat parts (b) and (c), but use an exact least squares fit of the logarithmscomputed in part (a).
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
A start-up firm has kept careful records of the time required to manufacture its
product, a shutoff valve used in gasoline pipelines.
Cumulative Number Number of Hours Required
of Units Produced for Next Unit
50 3.3
100 2.2
400 1.0
600 0.8
1,000 0.5
10,000 0.2
a. Compute the logarithms of the numbers in each column. (Use natural logs.)
b. Graph the ln(hours) against the ln(cumulative units) and eyeball a straight-line
fit of the data. Using your approximate fit, estimate a and b.
c. Using the results of part (b), estimate the time required to produce the first unit
and the appropriate percentage learning curve that fits these data.
d. Repeat parts (b) and (c), but use an exact least squares fit of the logarithms
computed in part (a).
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 5 images
