Question

2x1 + 4x2 + 7x3

c1: x1 +x2 +x3 ≤ 105

c2: 3x1 +4x2 +2x3 ≥ 310

c3: 2x1 +4x2 +4x3 ≥ 330

x1,x2,x3 ≥ 0

The problem was solved using a computer program and the following output was obtained

variabel	value	reduced cost	allowable increase	decrease
x1	0.0	-3.5	3.5	inf
x2	55	0	5	7
x3	60	0	inf	5

constraint	slack/surplus	dual price
1	0	10
2	0	-2
3	95	0

Constraint right-hand side sensitivity

constraint	allowable increase	current right hand	A decrease
1	55	100	22.5
2	115	310	100
3	80	330	inf

1. Create an Excel linear program and solve to confirm the optimal solution found by the previous computer program. (You do not need to perform the sensitivity analysis)

2. Which constraints are binding?

3. Suppose the profit from x2 is increased to $8. Is the above solution still optimal? Why?

4. We are not producing any of product x1. What is the minimum increase in the profit of x1 that would compel us to consider producing at least one x1?

Answer 1

Which constraints are binding?

Constraint 1 and 2 as they do not have any sack or surplus

Suppose the profit from x2 is increased to $8. Is the above solution still optimal? Why?

Yes as allowable increase of x2 is 5 which means any increase of profit level per unit to 4+5 = 9 would keep present solution optimal

We are not producing any of product x1. What is the minimum increase in the profit of x1 that would compel us to consider producing at least one x1?

reduced cost of x1 is -3.5 which means minimum increase of 3.5 is needed per unit to compel us to consider producing at least one x1