2. It takes exactly 26 paper clips laid end to end to make a length of 17 7/8 inches.
2 answers:
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Answer:
The artist should make 15 caricatures and 30 portraits.
Step-by-step explanation:
First, we identify the variables for the problem. In this case, the variables will be:
C=number of caricatures
P= number of portraits.
Next, we can use the variables to make the inequalities that constrain the problem.
We know the artist can't spend more than $360 for supplies and we also know that it costs $4 to make a caricature and $10 to make a portrait, so:
We also know the artist has a limit of time of 20 hours, which is the same as 20*60=1200 minutes to paint. We know it takes her 20 minutes to make a caricature and 30 minutes to make a portrait, so:
and we also know she must make a positive number of caricatures and a positive number of portraits so the other two constrains are:
So we can go ahead and graph them. (see attached picture)
Once we graphed the inequalities we can determine what the corners of the polygon created by the intersection of the shaded areas are, so we proceed and calculate them:
first point:
(0,0)
second point:
4(0)+10P=360
P=36
(0,36)
Third point:
20C+30(0)=1200
C=60
(60,0)
Fourth point:
We multiply the first equation by -5 so we get:
-20C-50P=-1800
20C+30P=1200
------------------------
-20P=-600
P=30
so:
20C+30(30)=1200
20C=1200-900
20C=300
C=15
(15,30)
Once we found the 4 points, we go ahead and evaluate them for the objective function. In this case, the objective function is the total amount of money she got from selling the pieces of art, so we get:
I=10C+20P
Point 1
I=10(0)+20(0)=0
Point 2
I=10(0)+20(36)=720
Point 3
I=10(60)+20(0)=600
Point 4
I=10(15)+20(30)=750
Next, we look for the greatest income which in this case will be 750 so that's why she must make 15 caricatures and 30 Portraits.
Answer:
a) 86%
b) 2nd unit = 82 hs.
3rd unit = 75 hs
c) 100th unit = 36 hs
Step-by-step explanation:
We can model the learning curve for manufacturing the units as:
where t is the time for the Xth unit, and a and b are parameters that we will calculate from the data,
We know that t(1)=95. Then, we have:
And we know that the fourth unit (X=4) take 71 hours to be completed (t(4)=71). Then, we can calculate the other parameter as:
We have the model for the learning curve:
The learning rate percentage is calculated from the b parameter:
The learning rate percentage is 86%.
b) The most likely times required for the 2nd and 3rd units are calculated with the model:
c) If we use the model to calculate the time required for the 100th unit, we have: