COB 291 Test 2 EXAM LATEST REAL EXAM QUESTIONS AND CORRECT ANSWERS WITH RATIONALES|ALREDY GRADED A+

COB 291 Test 2 EXAM LATEST REAL EXAM QUESTIONS AND CORRECT ANSWERS WITH RATIONALES|ALREDY GRADED A+ If the optimal value of a variable is basic (not zero), then the reduced cost is always: - ANSWER- zero If the optimal value of a variable is zero and the reduced cost corresponding to the variable is also zero, then: - ANSWER- ...there is at least one other corner that is also in the optimal solution. Reduced cost value is only non-zero when the optimal value of a variable is: - ANSWER- zero -The reduced cost value indicates: -In the case of a minimization problem, "improved" means: -In the case of a maximization problem, "improved" means - ANSWER- -how much the objective function coefficient on the corresponding variable must be improved before the value of the variable will be positive in the optimal solution. -reduced -increased Basic are? - ANSWER- non-zero Non basic are? - ANSWER- zero What is B sub i - ANSWER- the right hand side What is C sub j - ANSWER- the coefficient for X in the objective function What is A sub ij - ANSWER- the consumption ratio What is the shadow price of a redundant constraint? - ANSWER- zero What are shadow prices in forms of? - ANSWER- U How do you change the profit per item? - ANSWER- change C sub j In the sensitivity report how do you know if you have alternative optima? - ANSWER- • More than one 0 in the allowable inc/allowable dec in the decision variable section • A row of 0 in the reduced cost and final value of a decision variable • A row of 0 in the shadow price and final value of a constraint If the final value is positive then reduced cost is? - ANSWER- zero How do you know if it's a max/min by just looking at the reduced cost? - ANSWER- max - negative or o min - positive or 0 What tells you what you are paying above what you need to pay for a resource? - ANSWER- the shadow price If the final value = RHS what do you know exists? - ANSWER- a binding constraint E minus some number is? Why? - ANSWER- - virtually zero - the number is the exponent You can't have a negative amount of a resource because? - ANSWER- you have a nonneg. constraint on them How to formulate an LP model (five steps) - ANSWER- 1. Understand the problem. 2. Identify the decision variable. 3. State the objective function as a linear combination of decision variables. 4. State the constraints as linear combination of decision variables. 5. Identify any upper or lower bounds on the decision variables. What is pivoting? - ANSWER- moving from one extreme point to the next Where does Simplex start? How does it move? - ANSWER- starts us at the origin and mathematically takes us around the feasible region, from extreme point to extreme point, in the direction of the most improvement with respect to the objective function. Sensitivity analysis does what? - ANSWER- determines when a change in the parameters of a problems will cause a change in the basis. Basis is? - ANSWER- optimal solution What are the three parameters? - ANSWER- B sub i, C sub j, and A sub ij Shadow prices - ANSWER- the additional, or *marginal, value of one more unit of a resource.* If a basis changes, what else must change? (and visa versa) - ANSWER- the shadow prices and reduced cost What is right hand side ranging? - ANSWER- by how much can we change a righthand-side value without changing the basis. What is Cj ranging? - ANSWER- by how much can you change the Cj values without changing the basis. (MAX/MIN=4X1+5X2+9X3) How much can we change the 4, 5, or 9. Shadow price? How do you denote it? - ANSWER- marginal value of one more unit of a resource U sub i Right hand side value? Denoted? - ANSWER- amount of a resource B sub i Reduced cost? - ANSWER- the change in our Z value if we make one of our non basic decision variables a basic variable (unit contribution) Degeneracy? Page 154 - ANSWER- -*fewer basic variable than total constraints or if any of the allowable increase/decrease in the bottom part are zero you will have degeneracy* -means that some of your results in the sensitivity analysis might not be unique (A difference set of shadow prices and ranges might also pertain to the same problem and give you the same Z value for the problem, but not necessarily alternative optima) -*the solution to an LP problem is degenerate if the RHS values of the constraints have an allowable increase or allowable decrease of zero* DEGENERACY MAKES THE WAYS TO FIND ALTERNATIVE OPTIMA INACCURATE. IF YOU HAVE DEGENERACY YOU WILL NOT KNOW IF YOU HAVE ALTERNATIVE OPTIMA