Solve the following problem using graphical linear programming and answer the questions that follow. Use the simultaneous equations to determine the optimal values of the decision variables.
Maximize Revenue, Z = 6A +3B
Subject to
|
Material
|
20A
|
+
|
6B
|
≤
|
600lb
|
|
Machinery
|
25A
|
+
|
20B
|
≤
|
1,000hr
|
|
Labor
|
20A
|
+
|
30B
|
≤
|
1,200hr
|
|
|
|
|
A,B
|
≥
|
0
|
(i) What are the optimal values of the decision variables and Z?
(ii) Do any constraints have (nonzero) slack? If yes, which one(s) and how much slack does each have?
(iii) Does any constraints have nonzero surplus? If yes, which one(s) and how much surplus does each have?