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Topic 2 HW 2, Part 2
7.2 #5:
Solve problem 5 Using graphical analysis
Minimize ?? + ?? ?????????????? ????
??+?? ?6
3?? ? ?? ? 9
??, ?? ? 0
7.2 # 6:
Solve problem 6 Using graphical analysis
Maximize ?????? + ?????? ?????????????? ????
???? + ???? ? ???? (?????????? ? ???????? ???? ????????????)
???? + ?? ? ????
(?????????? ???? ??????????????????)
(????????????)
?????
??, ?? ? ??
(??????????????????????????
3.3 #2:
Use Equations
The Slope ?? =
The intercept
?? ? ???? ???? ?? ???? ? ????
?? ? ?????? ?(? ???? )
??=
??
? ?????? ? ???? ?? ???? ???? ? ????
?? ? ?????? ? (? ???? )
??
To estimate the coefficients of the line ?? = ???? + ?? such that the sum of the aquared
deviations between the line and the following data points is minimized.
a)
x
y
1.0
3.6
2.3
3.0
3.7
3.2
4.2
5.1
6.1
5.3
7.0
6.8
2
b)
x
y
29.1
0.0493
x
y
2.5
4.32
48.2
0.0821
72.7
0.123
92.0
0.154
118
0.197
140
0.234
165
0.274
199
0.328
5.0
6.79
5.5
7.23
c)
3.0
4.83
3.5
5.27
4.0
5.74
For each problem compute D and ???????? to bound ???????? .
4.5
6.26
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3.3 # 7:
Fit the data with the models given, using least squares
x
y
1
1
2
1
3
2
4
2
5
4
a) ?? = ?? + ????
b) ?? = ??????
3.3 #8:
Fit the data with the models given, using least squares
Data for stretch of a spring
x
y
5
0
10
19
a) ?? = ????
b) ?? = ?? + ????
c) ?? = ??????
20
57
30
94
40
134
50
173
60
216
70
256
80
297
90
343
100
390
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3.3 # 9:
Fit the data with the models given, using least squares
Data for the ponderosa pine
x
y
17
19
19
25
20
32
22
51
23
57
25
71
28
113
31
140
32
153
33
187
36
192
37
205
39
250
42
260
a) ?? = ???? + ??
b) ?? = ??????
c) ?? = ??????
3.4 # 7:
Producing Electronic Equipmentn electronics ?rm is producing three lines of products
for sale to the government: transistors, micromodules, and circuit assemblies. The ?rm has
four physical processing areas designated as follows: transistor production, circuit printing
and assembly, transistor and module quality control, and circuit assembly test and
packing. The various production requirements are as follows: Production of one transistor
requires 0.1 standard hour of transistor production area capacity, 0.5 standard hour of
transistor quality control area capacity, and $0.70 in direct costs. Production of micromodules requires 0.4 standard hour of the quality control area capacity, three transistors,
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and $0.50 in direct costs. Production of one circuit assembly requires 0.1 standard hour of
the capacity of the circuit printing area, 0.5 standard hour of the capacity of the test and
packing area, one transistor, three micromodules, and $2.00 in direct costs.
Suppose that the three products (transistors, micromodules, and circuit assemblies) may be
sold in unlimited quantities at prices of $2, $8, and $25 each, respectively. Thereare 200
hours of production time open in each of the four process areas in the coming month.
Formulate a mathematical model to help determine the production that will produce the
highest revenue for the ?rm.
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3.4 #7:
7. a. In the following data, W represents the weight of a ?sh (bass) and l represents its
length. Fit the model ?? = ?????? to the data using the least-squares criterion.
Length,
l (in)
Weight,
W (oz)
14.5
12.5
17.25
14.5
12.625
17.75
14.125
12.625
27
17
41
26
17
49
23
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b. In the following data, g represents the girth of a ?sh. Fit the model ?? = ???????? to the data
using the least-squares criterion
Length,
l (in)
14.5
Girth, g
9.75
(in)
Weight, 27
W (oz)
12.5
8.375
17
17.25
11.0
41
14.5
12.625
17.75
14.125
12.625
8.5
12.5
9.0
8.5
9.75
26
17
49
23
16
c. Which of the two models ?ts the data better? Justify fully. Which model do you prefer?
Why?

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