Use the following management scientist output to answer the questions.

Linear programming problem

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 costs
x1	13.333	0.000
x2	10.000	0.000
x3	0.000	10.889

constraint	slack/surplus	dual prices
1	0.000	-0.778
2	0.000	5.556
3	23.333	0.000

OBJECTIVE COEFFICIENT RANGES

variable	lowe limit	current value	upper limit
x1	30.000	31.000	no upper limit
x2	no	35.000	36.167
x3	no	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

a) give the solution to the problem.

b) which constraints are binding?

c) what would happen if the coefficient of x1 increased by 1?

d) what would happen if the right-hand side of constraint 1 increased by 10?