Answer Happy

Given the linear programming problem below where X1
represents the number of belts a company produces and X2
represents the number of pairs of gloves produced. The first
constraint is for the number of square yards leather available and
the second for the number of hours of skilled labor available.
Max z = 4X1 + 3X2
s.t. X1 + X2 ≤ 40
2X1 + X2 ≤ 60
The solution is X1 = X2 = 20 with max Z =
140. The final tableau is shown below
Z
X1
X2
S1
S2
RHS
Basis
1
0
0
2
1
140
Z =140
0
0
1
2
-1
20
X2 = 20
0
1
0
-1
1
20
X1 = 20
Use this information to answer the following questions.
1. Show that if c1, the coefficient of x1 in the objective
function, is between 1 and 5 the current basis remains optimal.