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[1] 



[2] 

Corner point with smallest xcoordinate 
Corner point with biggest xcoordinate 

Corner Point Coordinates : ( x , y ) 
( , )  ( , )  ( , ) 
Value of P = x + 3y 
[3]  Consider the problem in the box below : without solving it.  


(a)(3 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: 2 points for variables x and y, one point for the objective function (capital letter) 


(b)(2 pts) Using the best definition of variables from the choices in
[3a] 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 3point score on [3a] above in order to earn points in [3b]. Scoring below : Inequalities worth 1½ points, objective function worth ½ point 





I can help 
[5] 
Enter numbers of the SIMPLEX TABLEAU ( = ST ) for the problem at the right.
Continued in [6] below.
Scoring : bottom row worth 3 points, remaining 2 rows worth 1 point each 




[6] 


Final basic solution : 




row op name 

[7] [8] [9] 


[7] 
See alternate sample test as example of what [7][8][9] on your paper test will look like. Here (for 5 points), you must only enter the numbers of the SIMPLEX TABLEAU, as in [5] above. Scoring : bottom row worth 3 points, each other row worth 1 point 


[8] 
(6 points) Use SPECIFIC STEPS OF
SIMPLEX METHOD OUTLINED IN OUR CLASS HANDOUTS, to solve the problem in [7] above.
Enter numbers in decimal form to complete the needed 6 row operations below.
With correct work, you will encounter 2 pivots (3 row operations in each), both in
phase I of the
simplex method, at which point you will arrive at a FINAL TABLEAU.
All fractions in your matrices will have denominators 2,5, or 10:
no others; thus, decimals will terminate after one decimal place. Scoring : You must earn a perfect 5 points in [7] above before earning any points in [8]. One point for 1^{st} row op ; three points for the first 3 row ops ; 4 points for the first 4 row ops ; 6 points for all row ops.. 

[9]  (4 pts) You encountered 3 simplex tableaus in [8] above (starting, middle, and final), not counting intermediate matrices. The basic solution for the starting tableau is : x_{1} = x_{2} = 0, s_{1} = 2, s_{2} = 3, z = w = 0. Name the values of each of these variables for the middle and final tableaus: see diagram below. Scoring : 2 points for each fully correct basic solution 

1st pivoting 

2nd pivoting 

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