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example 5 Advertising and Sales
Chapter 6.5
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
a. Algebraically.
b. Graphically.
2009 PBLPathways
2009 PBLPathways
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
a. Algebraically.
b. Graphically.
2009 PBLPathways
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
a. Algebraically.
300100
15
100 15 300
1500 100 300
1500 200
7.5
x
x
x x
x x
x
x
x
y
(7.5, 100)
2 100y
1
300
15
xy
x
2009 PBLPathways
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
a. Algebraically.
300100
15
100 15 300
1500 100 300
1500 200
7.5
x
x
x x
x x
x
x
x
y
(7.5, 100)
2 100y
1
300
15
xy
x
2009 PBLPathways
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
a. Algebraically.
300100
15
100 15 300
1500 100 300
1500 200
7.5
x
x
x x
x x
x
x
x
y
(7.5, 100)
2 100y
1
300
15
xy
x
(15 + x)(15 + x)
2009 PBLPathways
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
a. Algebraically.
300100
15
100 15 300
1500 100 300
1500 200
7.5
x
x
x x
x x
x
x
x
y
(7.5, 100)
2 100y
1
300
15
xy
x
2009 PBLPathways
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
a. Algebraically.
300100
15
100 15 300
1500 100 300
1500 200
7.5
x
x
x x
x x
x
x
x
y
(7.5, 100)
2 100y
1
300
15
xy
x
2009 PBLPathways
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
a. Algebraically.
300100
15
100 15 300
1500 100 300
1500 200
7.5
x
x
x x
x x
x
x
x
y
(7.5, 100)
2 100y
1
300
15
xy
x
2009 PBLPathways
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
a. Algebraically.
300100
15
100 15 300
1500 100 300
1500 200
7.5
x
x
x x
x x
x
x
x
y
(7.5, 100)
2 100y
1
300
15
xy
x
2009 PBLPathways
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
a. Algebraically.
300100
15
100 15 300
1500 100 300
1500 200
7.5
x
x
x x
x x
x
x
x
y
(7.5, 100)
2 100y
1
300
15
xy
x
?
?
300 7.5100
15 7.5
2250100
22.5
100 100
2009 PBLPathways
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
a. Algebraically.
300100
15
100 15 300
1500 100 300
1500 200
7.5
x
x
x x
x x
x
x
x
y
(7.5, 100)
2 100y
1
300
15
xy
x
?
?
300 7.5100
15 7.5
2250100
22.5
100 100
2009 PBLPathways
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
a. Algebraically.
300100
15
100 15 300
1500 100 300
1500 200
7.5
x
x
x x
x x
x
x
x
y
(7.5, 100)
2 100y
1
300
15
xy
x
?
?
300 7.5100
15 7.5
2250100
22.5
100 100
2009 PBLPathways
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
b. Graphically.
100 15 300
1500 100
1
300
1500 200
7.5
50
300
0
1
x
x
x x
x x
x
x
x
y
2 100y
1
300
15
xy
x
2009 PBLPathways
100 15 300
1500 100
1
300
1500 200
7.5
50
300
0
1
x
x
x x
x x
x
x
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
b. Graphically.
x
y
(7.5, 100)
2 100y
1
300
15
xy
x
2009 PBLPathways
300100
15
100 15 300
1500 100 300
1500 200
7.5
x
x
x x
x x
x
x
Monthly sales y (in thousands of dollars) for Yang products are related to monthlyadvertising expenses x (in thousands of dollars) according to the function
Determine the amount of money that must be spent on advertising to generate $100,000in sales
300
15
xy
x
b. Graphically.
x
y
(7.5, 100)
2 100y
1
300
15
xy
x