Question

Solve these problems using graphical linear programming and answer the questions that follow. Use simultaneous equations to determine the optimal values of the decision variables.

a) Maximize Z = 2x₁ + 10x₂

_b) Maximize Z = 6A + 3B (revenue)

For both questions, answer the following:

(1)	What are the optimal values of the decision variables and Z?
(2)	Do any constraints have (nonzero) slack? If yes, which one(s) and how much slack does each have?
(3)	Do any constraints have (nonzero) surplus? If yes, which one(s) and how much surplus does each have?
(4)	Are any constraints redundant? If yes, which one(s)? Explain briefly.

I want to understand the concept; please explain what is being done.

Durability 10x +4x2 2 Strength Time 40 wk 6x2 24 psi lxi 2x2 14 hr X1 , X2 0 20A6B 600 lb Material Machinery Labor 25A 20B 000 hr 20A30B .200 hr A, B 0

Answer 1

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4) no constraints are redundant because, in each case all the constraints make up feasibile region and if any one of the constraints is not included, then optimal value gets affected.