Mathematics

Mathematics
excel

1.  A small manufacturing plant makes three types of inflatable boats: one-person, two-person, and
four-person models.  Each boat requires the services of three departments, as listed in the table.
The cutting, assembly, and packaging departments have available a maximum of 380, 330, and
120 labor-hours per week, respectively.

Department  One-Person Boat
(hours)
Two-Person Boat
(hours)
Four-Person Boat
(hours)
Cutting  0.5  1.0  1.5
Assembly  0.6  0.9  1.2
Packaging  0.2  0.3  0.5

How many boats of each type must be produced each week for the plant to operate at full
capacity?

2.   A food processing company produces regular and deluxe ice cream at 3 plants.  Per hour of
operation, the plant in Cedarburg produces 20 gallons of regular ice cream and 10 gallons of
deluxe ice cream.  Grafton plant produces 10 gallons of regular ice cream and 20 gallons of
deluxe ice cream, and the West Bend plant produces 20 gallons of regular ice cream and 20
gallons of deluxe ice cream.  It costs $70 per hour to operate the Cedarburg plant, $75 per hour
to operate the Grafton plant, and $90 per hour to operate the West Bend plant.  The company
needs at least 300 gallons of regular ice cream and at least 200 gallons of deluxe ice cream each
day.  How many hours per day should each plant operate in order to produce the required
amounts of ice cream and minimize the cost of production?  What is the minimum production
cost?

3.  The lengths (in centimeters) and girths (in centimeters) of 12 harbor seals is as follows:

Length,
x
137  168  152  145  159  159  124  137  155  148  147  146
Girth, y  106  130  116  106  125  119  103  104  120  110  107  109

Develop a linear regression model for these data and forecast the girth if length equals 164
centimeters.

4.  The weekly time spent (in hours) on homework for 18 randomly selected UHD enrolled in an
online ENGR 1400 class is as follows: 12.0, 11.3, 13.5, 11.7, 12.0, 13.0, 15.5, 10.8, 12.5, 12.3,
14.0, 9.5, 8.8, 10.0, 12.8, 15.0, 11.8, 13.0.
(a) Find the sample mean and the sample standard deviation.
(b) Construct a 99% confidence interval for the population mean.

5.  The degC() function to convert temperature in ℉ to ℃ is presented in Section 13.4 of the
textbook.  Write the companion function degF() that will convert temperature in ℃ to ℉.  Use
your function to convert 100℃, 37℃, 0℃, and -40℃  to℉.  Your solution should clearly show
the function.

6.  Write a VBA function that receives a gauge pressure and the barometric pressure and returns
the absolute pressure.  Have the function check whether the barometric pressure is zero,
indicating that the program should use a default value of 1 atmosphere as the barometric
pressure.  If the barometric pressure is zero, add 1 atmosphere (14.696 psia) to the gauge
pressure to calculate the absolute pressure.  Your solution should clearly show the function.
Test your solution for the following set of data:

(psi)

(psi)
0  12.9
10.3  14.696
2.5  1
2.5  0

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