Problem #2: Consider the following LP problem and its solution (refer to CDP#10).

MAX 4X1+6X2+7X3

S.T.

1) 3X1+2X2+5X3<120

2) 1X1+3X2+3X3<80

3) 5X1+5X2+8X3<160

4) +1X3>10

OPTIMAL SOLUTION

Objective Function Value = 166.000

Variable Value Reduced Costs

---------- ---------- ------------------

X1 0.000 2.000

X2 16.000 0.000

X3 10.000 0.000

Constraint Slack/Surplus Dual Prices

------------ ---------------- ----------------

1 38.000 0.000

2 2.000 0.000

3 0.000 1.200

4 0.000 -2.600

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit

---------- --------------- ----------------- ---------------

X1 No Lower Limit 4.000 6.000

X2 4.375 6.000 No Upper Limit

X3 No Lower Limit 7.000 9.600

Write your answer in blank lines.

3. What is the maximum profit? __________________

4. What is the value of X2 in the optimal solution? ________________

5. What is the number of less-than-or-equal to type constraints in the problem? ___________

6. If the resource corresponding to constraint 3 is offered at unit price of $1.00, would you be willing to buy it? _________ (answer yes or no)

7. If the profit from X1 gone up to 7.50 while the others remain at the current values, would there be a change in the optimal solution? __________ (answer yes or no)?