Simon makes and sells 75 layered, cotton masks at $16 each. For every $0.75 increase in cost of a mask, he will lose two sales. Determine the maximum revenue and the new selling price of a mask to achieve this maximum revenue.
Simon makes and sells 75 layered, cotton masks at $16 each. For every $0.75 increase in cost of a mask, he will lose two sales. Determine the maximum revenue and the new selling price of a mask to achieve this maximum revenue.
Related questions
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 |
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) 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?
