Question

finite mathematics an applied approach 11th edition, Sullivan, Chp 2, project page 101. // Should be in the book soulitions but can't find it. 1. You decide to compare the basic charges for two cell phone plans that include texting and Web access. Here are the monthly costs for two plans.* Plan A includes a flat rate of $39.99 for 450 anytime minutes plus $.02 for each text message (sent or received) and $1.99 per megabyte of data usage (50 mobile Web pages will incur data usage charges for about .3 megabytes). For Plan A, additional minutes above 450 minutes cost $.45 per minute. Plan B includes a flat rate of $44.99 for 500 anytime minutes plus $.04 for each text message and $2.29 per megabyte of data usage. For Plan B, additional minutes above 500 minutes cost $.50 per minute. The variables of the model are: x: the number of anytime minutes used per month. y: the number of text messages sent or received per month. z: the number of megabytes of data usage per month. A: the monthly cost for Plan A B: the monthly cost for Plan B - Assume that x >=450 and express A as a linear expression involving x, y, and z. - Assume that x >=500 and express B as a linear expression involving x, y, and z. - Suppose that 600 anytime minutes were used for a given month. Find the values of y and z so that A= B. Let z be a parameter. - Suppose that 600 anytime minutes and 5 megabytes of data usage were billed for a given month. Let y0 represent the number of text messages sent or received so that A= B for that month. Find y0. Determine which plan is less expensive for that month if y >y0. - You estimate that you will send or receive about 350 text messages per month and use 8 megabytes of data per month. Assuming that x>= 500, find the values of x for which A<= B. - You decide that you will spend about $100 per month for your cell phone plan. Set A = B = 100 and find valid solutions for the resulting system of equations. Let z be a parameter. Note that solutions are valid only when x>= 500, y>= 0, and z>= 0. - You estimate that you will use about 600 anytime minutes and require 3 megabytes of data usage in a given month. For what numbers of text messages would the cost of Plan B be less than or equal to the cost of Plan A for that month? - For what values of x will Plan A be less expensive than Plan B, if y = z = 0? - Suppose you learn of a third cell phone plan, Plan C, which includes unlimited text messaging and an unlimited data plan. The cost of Plan C is 59.99 for 500 anytime minutes. Each additional minute costs $.55 cents per minute. Let C represent the cost of Plan C. Find a linear expression for C in terms of the variables x, y, and z, assuming that x >=500. - If you expect to send or receive 450 text messages per month and use 10 megabytes of data per month, find the values of x for which C<= A and C <=B, assuming that x>= 500 -If you expect to send or receive 800 text messages per month and do not expect to use your cell phone to access the Web, find the values of x for which C<= A and C<= B, assuming x >=500. Then find the values of x for which A C and A B, assuming that x 500. - Suppose you expect to need between 600 and 1000 anytime minutes per month, an expect to send 400 text messages a month, and to have a data usage of about 8 megabytes per month. Determine which of the three plans (A, B, or C) would be the most economical.

Answer 1

39.99 +o 3g .9340.02 → +1.393 +(600-450) X 0,45 Given»-600. 3-5 and A+B Given and 44.9g o4 -293-D) Xo So loo

Solwi Given χ:.600 , 3:3 and B 2 A 39. 99 +0.029 +1.99x3 +(600-45o)Xo.45 44-99+00 * Siven 450)x04 * Given d> 800 go,

131.41 A 31 (29.31 B< 329 .31 114.99 Lc 334-99