For this scenario, the manager at Shooters needs to know how advertising will effect customer turn out. In other words, how much should he spend each week in order to get the biggest return on his money. To that end, the manager at Shooters also recorded data relating how much he spent on weekly advertisements, such as fliers and commercials, with how many customers he had each week.
Week
Ad $, a
People, q
Week
Ad $, a
People, q
Week
Ad $, a
People, q
1
$ 50
112
19
$ -
81
37
$ 200
195
2
$ 150
182
20
$ 300
190
38
$ 300
205
3
$ 200
188
21
$ 150
176
39
$ 250
193
4
$ 200
184
22
$ 50
127
40
$ 100
147
5
$ 150
167
23
$ 200
187
41
$ 50
123
6
$ -
77
24
$ 200
189
42
$ 250
191
7
$ 150
173
25
$ 300
203
43
$ 50
120
8
$ -
71
26
$ 150
168
44
$ -
89
9
$ 100
149
27
$ 100
153
45
$ 300
198
10
$ 200
193
28
$ 200
194
46
$ 200
189
11
$ 250
191
29
$ 200
182
47
$ -
82
12
$ 100
146
30
$ 250
200
48
$ -
87
13
$ 100
155
31
$ 50
125
49
$ -
76
14
$ 150
177
32
$ 300
189
50
$ 100
159
15
$ 50
124
33
$ 150
173
51
$ 50
121
16
$ 150
177
34
$ 300
205
52
$ 50
120
17
$ 100
148
35
$ 200
182
18
$ -
76
36
$ -
80
) Use this data to determine a model that describes the number of people q who come to Shooters as a quadratic function of the amount of money spent on ads.
Give a graph of the customer versus advertising data. Then state the formula that expresses how many customers he can expect based on advertising expenses, q(a).
2) Use the derivative of the quadratic function you found in question 1 to determine what amount should be spent on advertising each week in order for Shooters to achieve a maximum number of customers? How many customers would come if the owner spent the maximum on advertising?
For this scenario, the manager at Shooters needs to know how advertising will effect customer turn out. In other words, how much should he spend each week in order to get the biggest return on his money. To that end, the manager at Shooters also recorded data relating how much he spent on weekly advertisements, such as fliers and commercials, with how many customers he had each week.
| Week | Ad $, a | People, q | Week | Ad $, a | People, q | Week | Ad $, a | People, q |
| 1 | $ 50 | 112 | 19 | $ - | 81 | 37 | $ 200 | 195 |
| 2 | $ 150 | 182 | 20 | $ 300 | 190 | 38 | $ 300 | 205 |
| 3 | $ 200 | 188 | 21 | $ 150 | 176 | 39 | $ 250 | 193 |
| 4 | $ 200 | 184 | 22 | $ 50 | 127 | 40 | $ 100 | 147 |
| 5 | $ 150 | 167 | 23 | $ 200 | 187 | 41 | $ 50 | 123 |
| 6 | $ - | 77 | 24 | $ 200 | 189 | 42 | $ 250 | 191 |
| 7 | $ 150 | 173 | 25 | $ 300 | 203 | 43 | $ 50 | 120 |
| 8 | $ - | 71 | 26 | $ 150 | 168 | 44 | $ - | 89 |
| 9 | $ 100 | 149 | 27 | $ 100 | 153 | 45 | $ 300 | 198 |
| 10 | $ 200 | 193 | 28 | $ 200 | 194 | 46 | $ 200 | 189 |
| 11 | $ 250 | 191 | 29 | $ 200 | 182 | 47 | $ - | 82 |
| 12 | $ 100 | 146 | 30 | $ 250 | 200 | 48 | $ - | 87 |
| 13 | $ 100 | 155 | 31 | $ 50 | 125 | 49 | $ - | 76 |
| 14 | $ 150 | 177 | 32 | $ 300 | 189 | 50 | $ 100 | 159 |
| 15 | $ 50 | 124 | 33 | $ 150 | 173 | 51 | $ 50 | 121 |
| 16 | $ 150 | 177 | 34 | $ 300 | 205 | 52 | $ 50 | 120 |
| 17 | $ 100 | 148 | 35 | $ 200 | 182 | |||
| 18 | $ - | 76 | 36 | $ - | 80 |
|
) Use this data to determine a model that describes the number of people q who come to Shooters as a quadratic function of the amount of money spent on ads.
Give a graph of the customer versus advertising data. Then state the formula that expresses how many customers he can expect based on advertising expenses, q(a).
2) Use the derivative of the quadratic function you found in question 1 to determine what amount should be spent on advertising each week in order for Shooters to achieve a maximum number of customers? How many customers would come if the owner spent the maximum on advertising?
