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?