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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?

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[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
See Practice Example ?
General suggestions
  (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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