Given the following the LP: Min  Z=2x_1+3x_2 st

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Given the following the LP:

Min  Z=2x_1+3x_2

st.       2x_1+ x_2≥16     (1)

          x_1+?3x?_2≤36     (2)

          x_1+  x_2≥10     (3)

          x_1       ≤18     (4)

          x_1+ 2x_2≤ 5     (5)

          x_1        ≥ 0     (6)

                 x_2 ≥ 0     (7)

a) Draw the feasible region of this LP on a graph. Express the feasible region by its extreme points. (Give a letter name to all points on the graph.)

b) Which constraint/(s) are redundant and why?

c) What is the optimal solution? Express it as (x_1,x_2 )=z^*. Show the optimal point the graph. 

d) Indicate all of the corner point solutions and their feasibility or infeasibility. For feasible points, write down the objective functions. (Need a ?table as follows. You are going to decide how many points will be written on the table.)

 

Corner points (x_1,x_2 ) Feasibility Objective

 

......... ......... ......... .........

 

 

e) At optimal point, which constraint/(s) are binding/active and which constraint/(s) are non-binding/not active?

Constraint (1) = ......................

Constraint (2) = ......................

Constraint (3) = ......................

Constraint (4) = ......................

Constraint (5) = ......................

Constraint (6) = ......................

Constraint (7) = ......................