MAT 120 Lecture Notes - Lecture 1: Hyperbola, Fixed Cost, Scatter Plot

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emeraldcockroach191

23 Aug 2016

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1, 3, 5, 7, 15, 17, 25, 29, 35, 37, 39, 41ab, 43. **in section 2. 3, assume that the number of compounding periods is equal to the number of deposits, withdrawals, or payments. 1. 1: functions from the numerical, algebraic, and graphical viewpoints. * functions you should know/recognize on pages 50 & 51 (line, parabola, square root, cubic, hyperbola, etc. ) At least try p. 52 #3, 7, 15, 33, 39. Example: a car rental company charges ________ per mile, plus a ________ rental fee. * linear revenue function: revenue r of selling x items cost c of producing x items. )(xr profit p of producing and selling x items. Marginal cost: the company sells each t-shirt for ________. * demand function: demand _____ (# items demanded) as function of unit price _____ (price per item) * supply function: supply _____ (# items supplier willing to make available) as function of unit price _____

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Please explain answers

Please solve the circled 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?

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MAT 120 Lecture Notes - Lecture 1: Hyperbola, Fixed Cost, Scatter Plot

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