# Linear equation: Q1

#### San1998

##### New member
Hi,
I'm studying for a final of mine. I ran into a bit of trouble with this:
Use the following Management Scientist output to answer the questions.
LINEAR PROGRAMMING PROBLEM
Q1
MAX 31X1+35X2+32X3
S.T.
1) 3X1+5X2+2X3>90
2) 6X1+7X2+8X3<150
3) 5X1+3X2+3X3<120
OPTIMAL SOLUTION
Objective Function Value = 763.333
Variable Value Reduced Cost
X1 13.333 0.000
X2 10.000 0.000
X3 0.000 10.889
Constraint Slack/Surplus Dual Price
1 0.000 −0.778
2 0.000 5.556
3 23.333 0.000
OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
X1 30.000 31.000 No Upper Limit
X2 No Lower Limit 35.000 36.167
X3 No Lower Limit 32.000 42.889
RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
1 77.647 90.000 107.143
2 126.000 150.000 163.125
3 96.667 120.000 No Upper Limit
a. Give the solution to the problem.
b. Which constraints are binding?
c. What would happen if the coefficient of X1 increased by 3?
d. What would happen if the right-hand side of constraint 1 increased by 10?

ANS:
a.x1= 13.33, x2= 10, x3= 0, s1= 0, s2= 0, s3= 23.33, obj. func. = 763.33
b.Constraints 1 and 2 are binding.
c.The value of the objective function would increase by 40.
d.The value of the objective function would decrease by 7.78.

I need help with c and d. I don't quite understand how they solved it. May I get a step by step solution?