Identify the decision variables for this problem, using clear notation. Use these decision variables to formulate the firm’s objective function: Linear Equation Assignment, UOL, UK

Task 1

1. Identify the decision variables for this problem, using clear notation.
2. Use these decision variables to formulate the firm’s objective function, clearly stating what the objective is.
3. Use the information in Tables 1 and 2 above to identify the constraints for this problem.
4. Use what you have identified in 1-3 above to formulate and present the complete linear programming model for this problem.

Task 2

1. Enter the linear programming model you have derived in 4 above into Solver and obtain the optimal solution to the problem.
2. Extract the solution from Solver, state the value of the objective function and the values of the decision variables and summarise the results.

Task 3

1. Using Solver extract a Sensitivity Report for the problem.
2. Extract the slack and surplus variables from the Sensitivity Report and interpret their meaning.
3. Using the sensitivity report results indicates whether the problem’s optimal solution is unique or if there are alternative optimal solutions. Give reasons for your answer.
4. Present a brief interpretation of the ranging information on the objective function coefficients presented in the Sensitivity Report for this problem.

Task 4

1. Identify the shadow prices from the sensitivity report and interpret their meaning.
2. Using the shadow price on component 1 indicates the impact on the objective function of increasing its availability by 1 barrel. What is the upper limit of the availability of component 1 for which this shadow price is valid?
3. What would be the impact of increasing the availability of component 3 by 1 unit?