Below is the computer solution to a linear programming problem
linear programming:
Note: The Reduced Cost is often referred to as the
Coefficient Sensitivity.
For the above information, answer the following questions.
Provide your answers based on the above information and explain
your answers in terms of this information.
a) Write the objective function in equation form and write the
constraints as equalities or inequalities.
b) What are the values of the variables at optimality and what
is the value of the objective function at optimality?
c) If there was an opportunity to purchase additional units of
each resource (as expressed by the constraints), based on the
sensitivity analysis which resource(s) would you consider for
purchase? Why? Identify all of the resources that you would
consider. If you did not consider a resource for purchase, why did
you exclude it? Remember that Constraint 1 is equivalent to
Resource 1, Constraint 2 is Resource 2, and Constraint 3 is
Resource 3.
d) Suppose the contribution of variable X2 in the objective
function increases by 10. What are the values of the variables at
optimality now and what is the value of the objective function at
optimality with this change? Use the above sensitivity analysis in
answering this question and provide the sensitivity analysis
information you used.
Show transcribed image text RHS Shadow Price 40 Maximize 30 0.4 0.5 20 33.3 333 Constraint 1 Constraint 2 0.0 0.2 5 0 Constraint 3 0.6 0.3 21 44.4444 20 Solution 25 Sensitivity Analysis Value Reduced original Lower Upper Variable Value Bound Bound Cost X1 25 40 24 60 X2 20 30 20 50 Constraint Shadow Slackl original Lower Upper Price Surplus Value Bound Bound 0 14.00 33.3333 21.50 Constraint 1 20 Constraint 2 0 1 5 4.00 Infinity 21 18.75 30.00 0 Constraint 3 44.4444
RHS Shadow Price 40 Maximize 30 0.4 0.5 20 33.3 333 Constraint 1 Constraint 2 0.0 0.2 5 0 Constraint 3 0.6 0.3 21 44.4444 20 Solution 25 Sensitivity Analysis Value Reduced original Lower Upper Variable Value Bound Bound Cost X1 25 40 24 60 X2 20 30 20 50 Constraint Shadow Slackl original Lower Upper Price Surplus Value Bound Bound 0 14.00 33.3333 21.50 Constraint 1 20 Constraint 2 0 1 5 4.00 Infinity 21 18.75 30.00 0 Constraint 3 44.4444
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