The following linear programming problem has been solved by LINDO. Use the output to answer the questions. (Scroll down to see all).

LINEAR PROGRAMMING PROBLEM

MAX 41X1+52X2+21X3
S.T.
C.1) 5X1 + 5X2 + 9X3 < 1200
C.2) 11X1 + 14X2 + 5X3 < 1500
END

LP OPTIMUM FOUND AT STEP 1
OBJECTIVE FUNCTION VALUE
1) 5795.049
VARIABLE VALUE REDUCED COST
X1 0.000 0.217822
X2 74.247 0.000000
X3 92.079 0.000000
ROW SLACK OR SURPLUS DUAL PRICES
C.1) 0.000 0.336
C.2) 0.000 3.594
NO. ITERATIONS= 1
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 41.000000 0.217822 INFINITY
X2 52.000000 6.800000 0.297299
X3 21.000000 72.59999 1.466675
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
C.1 1200.000000 1500.000000 664.285706
C.2 1500.000000 1140.000000 833.333313

a.	Give the complete optimal solution (the values). (5 points)
b.	Which constraints are binding? (5 points)
c.	What is the dual price for the first constraint? What interpretation does this have? (5 points)
d.	Over what range can the objective function coefficient of X2 vary before a new solution point becomes optimal? (5 points)
e.	By how much can the amount of resource constraint 2 decrease before the dual price will change? (5 points)
f.	What would happen if the first constraint's right-hand side decreased by 200 and the second's increased by 400? (5 points) Hint: Perform the 100% rule test.