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MAT223H1 Study Guide - Divergence Theorem, Blackboard, Lagrange Multiplier

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School
UTSG
Department
Mathematics
Course
MAT223H1
Professor
Robert Brym

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Document Summary

Your instructor may be slightly ahead or behind this schedule. Your ability to correctly and completely solve the problems listed below is a very good indicator of your progress with the material. You are expected to solve at the very minimum all of the problems on this list. Lectures: chapter 12: functions of several variables, 12. 1 planes and surfaces, 12. 2. Graphs and level curves, 12. 3 limits and continuity. Section 12. 1: 3, 5, 11, 13, 15, 21, 23, 29, 35, 37, 41, 45, 49, 53, 57, 63, 67, 75, 79, 85. Section 12. 2: 3, 13, 17, 27, 34, 37, 39, 43, 47, 67. Section 12. 3: 7, 9, 11, 15, 19, 23, 25, 27, 29, 31, 33, 37, 41, 45, 47, 49, 53, 61, 63, 65, 69. Lectures: 12. 3 limits and continuity (continued), 12. 4 partial derivatives, 12. 5 the. Section 12. 4: 1, 7, 9, 15, 19, 21, 27, 33, 39, 41, 43, 45, 57, 59, 61, 63, 67, 69, 71, 75.

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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    

 

) 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?