Northeastern University Mathematical Model Questions Answer the 9 questions below. I only need answers one by one with word documents. 1. A dietitian in a

Northeastern University Mathematical Model Questions Answer the 9 questions below. I only need answers one by one with word documents. 1. A dietitian in a hospital is to arrange a special diet
composed of three basic foods. The diet is to include
exactly 180units of calcium, 100units of iron, and 220
units of vitamin A. The number of units per ounce of each special
ingredient for each of the foods is indicated in the table. Construct a
mathematical model to complete parts (A) through (C) below. Use
Gauss-Jordan elimination to solve the model and then interpret the
solution.
Units per Ounce
Food
A
Food
B
Food
C
Calcium
30
10
10
Iron
10
10
10
Vitamin
A
30
10
30
Construct a mathematical model for this situation. Let the first, second, and third equations represent
calcium, iron, and vitamin A, respectively. Let x 1 represent the number of ounces of food A, x 2represent
the number of ounces of food B, and x 3represent the number of ounces of food C.
x 1 plus+
x 2 plus+
x 3 equals=
x 1 plus+
x 2 plus+
x 3 equals=
x 1 plus+
x 2 plus+
x 3 equals=
(Type integers or decimals.)
(A) How many ounces of each food must be used to meet the diet requirements?
Therefore, the diet requires
ounces of food A,
ounces of food B, and
ounces of food C.
(Type whole numbers.)
(B) How is the diet in part (A) affected if food C is not used? Select the correct choice below, and, if
necessary, fill in the answer boxes to complete your choice.
A.
There is still one solution. The diet requires
of food B.
(Type whole numbers.)
ounces of food A and
ounces
B.
There are multiple solutions. If the diet uses t ounces of food B, it should use
food A, where t is an integer satisfying
ounces of
less than or equals?tless than or equals?
.
C.
There are no solutions. There is no combination of foods that will meet the diet requirements exactly.
(C) How is the diet in part (A) affected if the vitamin A requirement is dropped? Select the correct choice
below, and, if necessary, fill in the answer boxes to complete your choice.
A.
There is still one solution. The diet requires
ounces of food B, and
(Type whole numbers.)
ounces of food A,
ounces of food C.
B.
There are multiple solutions. If the diet uses t ounces of food C, it should use
food A and
ounces of food B, where t is an integer satisfying
equals?tless than or equals?
ounces of
less than or
.
C.
There are no solutions. There is no combination of foods that will meet the diet requirements exactly.
2.
3.
4. A company with manufacturing plants located in State A and State B has labor-hour and wage requirements for
the manufacture of three types of inflatable boats as given in the two matrices below. Complete parts (A) through (D).
Hourly Wages
State A State B
17.69
18.33 Cutting Dept
Labor-Hours Per Boat
Cutting DeptAssembly DeptPackaging Dept
0.8
1-person boat
0.4
0.6
N=
1.4
13.57
16.33 Assembly Dept M=
0.9
1.5
1.5
11.96
11.19 Packaging Dept
1.2
1.9
(A) Find the labor costs for a one-person boat manufactured at the State A plant.
Labor
2-person boat
4-person boat
costs=$
(Round to the nearest cent as needed.)
(B) Find the labor costs for a four-person boat manufactured at the State B plant.
Labor
costs=$
(Round to the nearest cent as needed.)
(C) Discuss possible interpretations of the elements in the matrix products MN and NM. Select the correct
choice below that describes the best interpretation of the elements in the matrix product MN.
A.
Matrix product MN exists and represents the labor cost for cutting department for the three types of
inflatable boats for state A and state B.
Your answer is not correct.
B.
Matrix product MN exists and represents the total labor cost for the three types of inflatable boats for each
state.
This is the correct answer.
C.
Matrix product MN exists and represents the labor cost for assembly and packaging departments for the
three types of inflatable boats for state A and state B.
D. Matrix product MN does not exist.
Select the correct choice below that describes the best interpretation of the elements in the matrix product
NM.
A.
Matrix product NM exists and represents the labor cost for cutting department for the three types of
inflatable boats for state A and state B.
B.
Matrix product NM exists and represents the total labor cost for the three types of inflatable boats for each
state.
C.
Matrix product NM does not exist.
D.
Matrix product NM exists and represents the labor cost for assembly and packaging departments for the
three types of inflatable boats for state A and state B.
(D) If the product MN has a meaningful interpretation, find the product and label its rows and columns.
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice that
represents the matrix product MN.
A.
Labor cost per boat
1- person
2- person
boat
boat
State A
State B
State C
B.
Labor cost per boat
State A
State B
1-person boat
2-person boat
4-person boat
C.
MN cannot be determined.
If the product NM has a meaningful interpretation, find the product and label its rows and columns. Select
the correct choice below and, if necessary, fill in the answer boxes to complete your choice that
represents the matrix product NM.
A.
Labor cost per boat
1-person boat 2-person boat
State A
State B
State C
B.
Labor cost per boat
State A
State B
1-person boat
2-person boat
4-person boat
C.
NM cannot be determined.
5. A concert hall has 12,000 seats and two categories of ticket prices, $15 and $35.
Assume that all seats in each category can be sold.
Concert
1
2
3
Tickets sold
12,000
12,000
12,000
Return required
$182,000
$265,000
$300,000
a. How many tickets of each category should be sold to bring in each of the returns indicated in the table?
$15
$35
Tickets
Tickets
Concert 1
Concert 2
Concert 3
b. Is it possible to bring in a return of $162,000 when all the seats are sold?
A.
No, $162,000 is greater than the highest possible return.
B.
No, $162,000 is less than the smallest possible return.
C.
Yes, $162,000 is within the range of possible returns.
D.
None of the above.
Is it possible to bring in a return of $373,000 when all the seats are sold?
A.
No, $373,000 is less than the smallest possible return.
B.
Yes, $373,000 is within the range of possible returns.
C.
No, $373,000 is greater than the highest possible return.
D. None of the above.
c. Describe all the possible returns. Choose the correct answer below.
A.
The return can be any multiple of $10.
B.
The return can range from $234,000 to $324,000 in steps of $10.
C.
The return can range from $234,000 to $324,000 in steps of $62.
D.
None of the above.
6.
7. A biologist has available two commercial food mixes containing the percentage of protein and fat given
in the table. Complete parts (A) and (B) below.
Mix Protein(%) Fat(%)
A
20
4
B
14
3
(A) How many ounces of each mix should be used to prepare each of the diets listed in the following
table?
Diet
1
2
3
Protein 79
oz
Fat
16
oz
92
oz
19
oz
99
oz
21
oz
For Diet 1, there should be
(Simplify your answer.)
oz of mix A and
oz of mix B.
For Diet 2, there should be
(Simplify your answer.)
oz of mix A and
oz of mix B.
For Diet 3, there should be
(Simplify your answer.)
oz of mix A and
oz of mix B.
8. The economy of a small island nation is based on two sectors, coal and steel. Production of a dollar’s
worth of coal requires an input of $ 0.2from coal and $ 0.25 from steel. Production of a dollar’s worth of
steel requires an input of $0.56 from coal and $0.20 from steel. Find the output from each sector that is
needed to satisfy a final demand of $40 million for coal and $58 million for steel.
The output from the coal sector is approximately
$
million.
(Round to the nearest million.)
The output from the steel sector is approximately
$
; ; million.
(Round to the nearest million.)
9. The economy of a small island nation is based on two sectors, agriculture and tourism. Production of a
dollar’s worth of agriculture requires an input of $ 0.35 from agriculture and $ 0.40from tourism.
Production of a dollar’s worth of tourism requires an input of
$ 0.43from agriculture and $ 0.12from
tourism. Find the output from each sector that is needed to satisfy a final demand of $ 31million for
agriculture and $ 71million for tourism.
The output from the agriculture sector is approximately
$
million.
(Round to the nearest million.)
The output from the tourism sector is approximately
$
million.
(Round to the nearest million.)

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