Question

150 constraint 1 30 X + 10 Y = 1500 Constraint 2 10 X + 10 Y = 1000 100 Constraint 3 X> 50 50 50 100 150 0 Constraints 1 and 2 are binding, with the optimal solution at Point G. How much can be removed from Constraint 1's resources (RHS) before its shadow price is no longer valid? [Enter your answer as a magnitude rounded to the nearest integer. NOTE: There is a typo in the chart above. X250 should read as Y250

Answer 1

150 Constraint 1 30 X + 10 Y 1500 Constraint 2 10 X + 10 Y 1000 100 Constraint 3 X250 50 D 0 50 100 150

The above two red lines represent the region of feasibility i.e. the range of the RHS values for which the shadow price remains unchanged.

The question asks for the lower limit of this range (as it uses the term 'removed').

So, we need to find the RHS of the lower red line at the. Let the RHS be 'C'. The slope is same as the original constraint.

30 X + 10 Y = C

Note that the line passes through (0, 100) so that the above equation becomes

30*0 + 10*100 = 1000

So, the equation of the line is 30 X + 10 Y = 1000

So, the RHS of the original constraint can be reduced by (1,500 - 1,000) = 500 before changing the shadow price.