TORA Experiment. Consider the following LP model: Maximize z = 5x1 + 4x2
subject to
6x1 + 4x2 … 24
6x1 + 3x2 … 22.5
x1 + x2 … 5
x1 + 2x2 … 6
-x1 + x2 … 1
x2 … 2
x1, x2 Ú 0
In LP, a constraint is said to be redundant if its removal from the model leaves the
feasible solution space unchanged. Use the graphical facility of TORA to identify the
redundant constraints, and then show that their removal (simply by not graphing them)
does not affect the solution space or the optimal solution.

y = x + 95

y = 42 + 95

y=137 mm hg

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

42

step-by-step explanation: