Below is the computer solution to a linear programming problem linear programming:

	X1	X2		RHS	Shadow Price
Maximize	40	30
Constraint 1	0.4	0.5	<=	20	33.3333
Constraint 2	0.0	0.2	<=	5	0
Constraint 3	0.6	0.3	<=	21	44.4444
Solution	25	20
Sensitivity Analysis
Variable	Value	Reduced Cost	Original Value	Lower Bound	Upper Bound
X1	25	0	40	24	60
X2	20	0	30	20	50
Constraint	Shadow Price	Slack/ Surplus	Original Value	Lower Bound	Upper Bound
Constraint 1	33.3333	0	20	14.00	21.50
Constraint 2	0	1	5	4.00	Infinity
Constraint 3	44.4444	0	21	18.75	30.00

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.