Optimal Solution

Assume both X and Y must be non-negative!

Given:

Max Z = 2x + 2y

ST

3x + y <= 6

x + 4y <= 8

(1) Create a graph

(2) Find the corner points

(3) Which is the optimal solution?

(4) What are the ratios of the coefficients of x to y that change which corner point is optimal?

(5) What is the current ratio?

(6)How much can you increase or decrease the coefficient of x without changing the optimal solution?

(7) What range of values will cause each corner point to become the optimal solution?

(8) Are there values for which there are multiple optimal solutions?

(9) By how much can you change each constraint’s right hand side before the current basis changes?

(10) Does changing each constraints right hand side increase profit? Do some changes result in a decrease?

(11) How much should you be willing to pay for a unit increase in a particular right hand side value?

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