MATH 132 UNLV Number of Type Souvenirs & Objective Function Maximized Problem

A woman has up to $10000to invest. Her broker suggests investing in two bonds: B
ond A , and Bond B.
Bond A is a rather risky bond with an annual yield of 10% and bond B is a rather safe bond with an annual yield of 7% After some consideration, she decides to invest at most $6000 in bond A, and invest at least $2000 in bond B. Moreover, she wants to invest at least as much in bond A as in bond B. She wishes to maximize her annual yield.

a) I
n each blank box below, select the best answer from the list that helps complete the objective function and its associated constraint inequalities. Please note that the option <= indicates≤≤, and the option >= indicates≥≥.

R= [ Select ] 0.07 6000 0.1 10000 2000 Correct answer is not listed A+ [ Select ] Correct answer is not listed 10000 2000 0.1 6000 0.07 B

A+ [ Select ] Correct answer is not listed 2 1 0.07 0.01 2000 6000 B [ Select ] <= >= = Correct answer is not listed 10000

A [ Select ] Correct answer is not listed <= = >= 6000

B [ Select ] Correct answer is not listed <= >= = 2000

A [ Select ] Correct answer is not listed <= >= = B

b) Use the geometric approach (with A placed on the x-axis and B on the y-axis) to determine the coordinates of the corner points of the solution region. Then, select the answer from this list: [ Select ] (6000,4
000) , (6000,2000) , (8000,2000) (0,0) , (0,10000) , (10000,0) Correct answer is not listed (0,10000) , (0,2000) , (6000,2000) , (6000,4000) (6000,0) , (6000,2000) , (8000,2000) , (10000,0) (0,0) , (0,2000) , (6000,2000) , (6000,0) (6000,0) , (6000,4000) , (10000,0)

c) Which of the feasible corner points you selected in part (b) above maximizes the objective function? Note that a feasible corner point is any corner point with at least one non-zero coordinate. Select the answer from this list: [ Select ] (6000,0) Correct answer is not listed (8000,2000) (6000,4000) (0,10000) (6000,2000) (10000,0)

d) What is the maximum yield? [ Select ] $740 $8
40 Correct answer is not listed $700 $800 $920 $880

d

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Read the information below and construct the objective function, and the associated constraint inequalities. DO NOT SOLVE THE MAXIMUM PROBLEM.

Ace Novelty wishes to produce two types of souvenirs: type A and type B . The sale of each type A souvenir will result in a profit of $2 , and the sale of each type B souvenir will result in a profit of $3
. To manufacture a type A souvenir requires 3minutes on machine I and 4
minute on machine II
. On the other hand, a type B souvenir requires 2 minute on machine I and 5
minutes on machine II. There are at most 2 hours available on machine I , and at most 4 hours available on machine II.

Construct the objective function for maximizing profit, and construct the associated constraint inequalities by selecting the appropriate symbol or number from the dropdown list.

Note: The symbol <= in the dropdown list indicates "less than or equal to“, and the symbol >= in the dropdown list indicates “greater than or equal to“.

Hint: Make sure that all units of time are converted to minutes.

P= [ Select ] [“4”, “>=”, “1”, “120
“, “5”, “2”, “<=", "0", "3", "240
“, “7”] A+ [ Select ] [“0”, “<=", "240", "4", "3", "7", "5", "6", "120", "1", ">=”] B

[ Select ] [“>=”, “7”, “120”, “240”, “<=", "6", "4", "2", "1", "3", "0"] A+2B
[ Select ] [“5”, “>=”, “<=", "3", "6", "4", "240", "120", "7", "0", "1"] 120

4A+
[ Select ] [“5”, “>=”, “3”, “240”, “6”, “4”, “<=", "120", "0", "7", "1"] B [ Select ] ["240", "1", ">=”, “<=", "5", "3", "6", "120", "7", "4", "0"] 240

A [ Select ] [“=”, “<=", ">=”] 0

B [ Select ] [“<=", "=", ">=”] 0

don

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A store sells two types of toys: toy A and toy B. Each toy A costs the store owner $8 to purchase, and each toy B costs her $16
. Each toy A brings the owner of the store a profit of $2 , while each toy B yields a profit of $3. The store owner estimates that no more than 2000 toys will be sold every month, and she does not plan to invest more than $20000 in inventory of these toys. She would like to maximize her monthly profit.

a) In each blank box below, select the best answer from the list that helps complete the objective function and its associated constraint inequalities. Please note that the option <= indicates ≤≤ , and the option >= indicates ≥≥.

P= [ Select ] [“2”, “1”, “16”, “3”, “Correct answer is not listed”, “8”] A+ [ Select ] [“16”, “3”, “2”, “1”, “Correct answer is not listed”, “8”] B

A+ [ Select ] [“3”, “1”, “16”, “8”, “Correct answer is not listed”, “2”] B [ Select ] [“>=”, “<=", "=", "Correct answer is not listed"] 2000

[ Select ] [“Correct answer is not listed”, “2”, “16”, “3”, “1”, “8”] A+16B
[ Select ] [“=”, “<=", ">=”, “Correct answer is not listed”] 20000

b) Use the geometric approach (with A placed on the x-axis and B on the y-axis) to determine the coordinates of the corner points of the solution region. Then, select the answer from this list: [ Select ] [“(0,1250) , (0,2000) , (1500,500)”, “(0,0) , (0,1250) , (1500,500) , (2000,0)”, “(0,0) , (0,1250) , (2500,0)”, “(0,0) , (0,2000) , (1500,500) , (2000,0)”, “(1500,500) , (2000,0) , (2500,0)”, “Correct answer is not listed”, “(0,0) (0,2000) , (1500,500) , (2500,0)”]

c) Which of the feasible corner points you selected in part (b) above maximizes the objective function? Note that a feasible corner point is any corner point with at least one non-zero coordinate. Select the answer from this list: [ Select ] [“Correct answer is not listed”, “(2000,0)”, “(1500,500)”, “(2500,0)”, “(0,2000)”, “(0,1250)”]

d) What is the maximum monthly profit? [ Select ] [“$3850”, “$3750”, “Correct answer is not listed”, “$4500”, “$4800”, “$4000”]