Maximization Problem

chwala

Hi Mathematicians,
I recently encountered this problem in maximization...
Maximize 1170X1 + 1110X2
Subject to
1. 9x1 +5x2 ≥ 500
2. 7x1 +9x2 ≥ 300
3. 5x1 + 3x2 ≤ 1500
4. 7x1 + 9x2 ≤ 1900
5. 2x1 + 4x2 ≤ 1000
X1,X2 ≥ 0

Where it was stated that 9x1 +5x2 ≥ 500 and 7x1 + 9x2 ≤ 1900 are the two constraints forming the feasible region…I was just wondering why the two…..
IN
1. When x1 =0 x2 = 100, when x2 =0 x1=55.556….i n (2) x1=42.85 x2=33.33 evidently x1,x2 in (1) is bigger than (2)
2. In (4) x1=271.42 x2=211.11
In (5) x1=500 x2=250 a problem here why is 4 taken as one of the constraints and yet the values of x1 and x2 in 5 are greater than in 4 ?
Am puzzled…

HallsofIvy

What you are saying is that some of the constraints are unnecessary- they do not put any additional restriction on the feasible area. Just ignore them. I presume that in what ever application this is from, there was some condition that might have a restraint on the feasible area, but, it turns out, others cover that.

chwala

thanks i have figured out the problem.