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Math 76O-143 Finite Mathematics
Self-marking Homework Assignment #3

(Inequalities, Worded Problems)
Submit over the internet by 11:59 PM on Sunday 28 February 2016
Maximum value toward semester grade is 2 pts
Methods will be discussed in class;
CAUTION: Prof McFarland makes new tests each semester.
 Average grade on Fall 2015 paper test #3 : 6.58 Perfect = 10 See future grade prospects?

 Click or type the appropriate answer for each question. When you are sure of your answers, send them to your Professor: Enter your name above Enter preferred email address;include @ and whatever follows Enter student I.D.
[1] (a)(2 pts) At the right are the graphs of 5 lines : the 2 axes and 3 others in color. These are the graphs of the equations associated with the inequalities boxed below. Click any or all boxes which are located in the solution set of the adjacent system of inequalities.
On paper tests, students must create these graphs without a graphing calculator.
 x + y 10 3x + y 12 -2x + 3y 3 x 0 y 0
(b)(3 pts) Exactly one of the points A, B, C (figure at right) is a corner point of the solution set of the boxed system at the right.
Enter the coordinates of that corner point :
( , )
[2] Consider the problem in the 2 boxes below : without solving it.

 GAS sorority is selling lasagna and pizza to raise money. The number of minutes required from Anne, Betty, and Christy for each serving of these foods, and the profit per serving, is given in the table below. Anne can work at most 900 minutes, Betty can work at most 1080 minutes, and Kristy can work at most 840 minutes. How many servings of each food should GAS sorority make to maximize its profit?

 Minutes of Anne's time needed Minutes of Betty's time needed Minutes of Kristy's time needed Profit one serving of lasagna 2 3 2 \$18 one serving of pizza 1 1 2 \$12
(a)(2 pts) In the box below are various ways to define variables in solving the above problem. Choose one or more of these definitions of variables, so that taken together, your choices would be the best in solving the problem above.
On paper tests, you must write definitions rather than choose among options.
Scoring: one point for objective function (capital letter), one point for all other variables

 Let x = number of minutes Anne must work Let y = number of minutes Betty must work Let z = number of minutes Christy must work Let x = number of servings Anne must make Let y = number of servings Betty must make Let z = number of servings Christy must make Let x = profit on food made by Anne Let y = profit on food made by Betty Let z = profit on food made by Christy Let S = total number of servings of both foods Let x = number of servings of lasagna made Let y = number of servings of pizza made Let x = lasagna Let y = pizza Let x = profit on lasagna made by the sorority Let y = profit on pizza made by the sorority Let A = total amount of food of both types Let M = total number of minutes needed Let P = total profit on sales of both food types Let P = profit
(b)(2 pts) Using the best definition of variables from the choices in [2a] above, choose one or more of the options below to assemble a correct translation of the original problem into a set of inequalities and objective function below.
You must first earn a perfect 2-point score on [2a] above in order to earn points in [2b].
Scoring below : Inequalities worth 1½ points, objective function worth ½ point

 2x + 3y + 2z 18 2x + 3y + 2z = 18 x + y + 2z 12 x + y + 2z = 12 2x + y 900 3x + y 1080 2x + 2y 840 x 900 y 1080 z 840 x 0 y 0 z 0 x 0 y 0 z 0 M = 2x + 3y + 2z M = 900x + 1080y + 840z P = 18x + 12y S = x + y
(c)(1 pt) The solution set of a system of inequalities consists of a quadrangle with vertices at (0,6), (4,10), (12,8), and (15,0). What is the largest value of Z = x + 4y if x and y must satisfy all these inequalities?
Largest value of Z is :   Z =

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