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

COB 291 Test 2 EXAM QUESTIONS AND ANSWERS WITH RATIONALES|ALREDY GRADED A+ What one constraint does every LP problem have? - ANSWER- Non-negativity If an LP problem has decision variables that represent proportions or percentages, what constraint(s) must be included? - ANSWER- • Non-negativity • Sum of Decision Variables = 1 What are key characteristics of Mixing/Blending Problems? - ANSWER- • When writing objective function/constraints, percentages representing parameters are generally turned into decimals for purposes of the problem & coming up with an ANSWER that actually makes sense The decision variables are what you as the decision maker have __________ __________. - ANSWER- control over • A _____________ variable is a non-zero variable. • A _____________ variable is a zero variable. • When a constraint is used to capacity, then it is a _______________ constraint or a ______________ variable. • When a resource is not used to capacity, then it is a ______________ variable. • If you have a surplus or a slack constraint, then you have a ____________ variable. - ANSWER- • A *basic* variable is a non-zero variable. • A *non-basic* variable is a zero variable. • When a constraint is used to capacity, then it is a *binding* constraint or a *non-basic* variable. • When a resource is not used to capacity, then it is a *basic* variable. • If you have a surplus or a slack constraint, then you have a *basic* variable. • A ___________ occurs when you have used more than the minimum amount required. • A ___________ occurs when you have used less than the maximum possible amount available. • A ___________ occurs when you have used the amount of resource available. • A ___________ occurs when you have used the amount required of a resource. - ANSWER- • A* surplus* occurs when you have used more than the minimum amount required. • A *slack* occurs when you have used less than the maximum possible amount available. • A *slack* occurs when you have used the amount of resource available. • A *surplus* occurs when you have used the amount required of a resource. • What is a shadow price? • When will the shadow price ALWAYS be zero? • When the shadow price is *not* zero, what type of constraint do you have? • When maximizing profit, shadow prices are above and beyond what you are already paying for a_______________. - ANSWER- • Marginal Value (in terms of contribution to Z-value) of a Resource •w/non-binding/redundant constraint •binding •resource. ___________ is the process of starting at the origin and moving from point to point around the feasible region in order to find the optimal solution. - ANSWER- Simplex model ___________ is the action of moving from one extreme (/________) point to another. - ANSWER- - pivoting - corner Sensitivity analysis determines when a change in a ____________ will cause a change in the basis. - ANSWER- parameters For a maximization problem, we will only produce a new item if the item's unit contribution is __________________. - ANSWER- positive • The basis changes when an objective function coefficient is changed to a value outside of the ______ range or a constraint is changed to a value outside of the _____/_____ range. When the basis changes, so do the decision variables' ________ ___________ and the resource's ___________ ______________. - ANSWER- The basis changes when an objective function coefficient is changed to a value outside of the *Cj* range or a constraint is changed to a value outside of the *RHS/bi* range. When the basis changes, so do the decision variables' *reduced costs* and the resource's *shadow prices* • If we are considering changing the amount of a constraint, we need to look at the _____ range. - ANSWER- Bi/RHS • If we are considering changing the price of our product (decision variable), we need to look at the ________ range. - ANSWER- C sub j • If the coefficient of the objective function is changed to a value inside the allowable range, will the basis change? ________ What if the value is on the border of the allowable range? ________ i. Will the final Z value change? If so, by how much? - ANSWER- - no - No, except there would be alternative optima indicating that more than one combination of basic variables would result in the same Z value corresponding to that particular Cj value -Yes - (new Cj - old Cj) * amount of Xi produced 1. Reduced cost represents how much each __________ ___________ ____________ would have to improve before the corresponding __________ ___________ could assume a positive (__________) value in the optimal solution. • It also represents how much the Z value will increase/decrease if we decide to produce a product we _____ _____ currently ____________. • In a minimization problem, improvement refers to a ___________ in the objective function coefficient. • In a maximization problem, improvement refers to an ___________ in the objective function coefficient. • In a minimization problem, the range for a reduced cost is: ____________ • In a maximization problem, the range for a reduced cost is: ____________ - ANSWER- 1. Reduced cost represents how much each *objective function coefficient* would have to improve before the corresponding *decision variable* could assume a positive *(basic)* value in the optimal solution. • It also represents how much the Z value will increase/decrease if we decide to produce a product we *do not* currently *produce.* • In a minimization problem, improvement refers to a *decrease* in the objective function coefficient. • In a maximization problem, improvement refers to an *increase* in the objective function coefficient. • In a minimization problem, the range for a reduced cost is: *(0,infinity)* • In a maximization problem, the range for a reduced cost is: *(neg infinity, 0)* Unit contribution is another name for __________ ___________, and is calculated from (choose one: aij, bi, and Cj) _____ - _____________ _______________. - ANSWER- Unit contribution is another name for *reduced cost*, and is calculated from (choose one: aij, bi, and Cj) *Cj - opportunity cost* The opportunity cost is calculated by.... - ANSWER- take A sub ij and multiply it by U (shadow price) for all constraints. Sum all of these. For a minimization problem, we will only produce a new item if the item's unit contribution is __________________. - ANSWER- negative If final value is basic, reduced cost is? - ANSWER- non-basic