Problem:
Solve the problem using graphical linear programming and answer the questions that follow.
Maximize Z= 2x + 10y
Subject to
Durability 10x + 4y >= 40 wk
Strength 1x + 6y >= 24psi
Time 1x + 2y <= 14 hr
x,y >= 0
Required:
Question 1) What are the optimal values of the decision variables and Z?
Question 2) Do any constraints have (nonzero) slack? If yes, which one(s) and how much slack does each have?
Question 3) Do any constraints have (non zero) surplus? If yes, which one(s) and how much surplus does each have?
Question 4) Are any constraints redundant? If yes, which one(s)? Explain briefly.
Solve the given numerical problem and illustrate step by step calculation.