ACCA F5: Strategic Decision-Making with Limiting Factors

1. What are the five steps using key factor analysis if there is one limiting factor?

The correct answer involves identifying the bottleneck constraint, calculating the contribution per unit for each product, calculating the contribution per unit of the bottleneck resource for each product, ranking the products in order of the contribution per unit of the bottleneck resource, and allocating resources based on this ranking.

Explanation

The correct answer involves identifying the bottleneck constraint, calculating the contribution per unit for each product, calculating the contribution per unit of the bottleneck resource for each product, ranking the products in order of the contribution per unit of the bottleneck resource, and allocating resources based on this ranking.

2. What are shadow (duel) prices, how is the shadow cost found, and what about non-critical constraints?

The shadow cost is determined by dividing the total cost by the number of constraints in the model

Non-critical constraints will have higher shadow prices compared to critical constraints

Shadow prices are the lowest cost at which resources can be acquired

Shadow prices represent the opportunity cost of resources and are not the actual cost of acquiring them. The shadow cost is not simply an average cost calculation but is based on the increase in value from an additional unit of a resource. Non-critical constraints having zero shadow prices indicate that they are not constraining factors in the optimization model.

Explanation

Shadow prices represent the opportunity cost of resources and are not the actual cost of acquiring them. The shadow cost is not simply an average cost calculation but is based on the increase in value from an additional unit of a resource. Non-critical constraints having zero shadow prices indicate that they are not constraining factors in the optimization model.

3. How to calculate shadow costs?

3. The shadow price for a constraint can be calculated by subtracting the constraint's slack from the optimal solution value.

2. Shadow costs are directly proportional to the number of constraints in a linear programming problem.

1. By randomly assigning values to constraints and analyzing the impact on the optimal solution.

Understanding how to calculate shadow costs involves following a specific process involving adjustments to constraints and simultaneous equations to derive the shadow price accurately.

Explanation

Understanding how to calculate shadow costs involves following a specific process involving adjustments to constraints and simultaneous equations to derive the shadow price accurately.

4. What are the implications of shadow prices and slack?

The feasible region remains unchanged regardless of changes in shadow prices

Shadow prices are fixed values that cannot be adjusted

Shadow prices have no impact on management decision-making

The correct answer highlights the importance of shadow prices in determining the maximum premium for a scarce resource and the necessity of considering them carefully. The incorrect answers provide false statements that do not align with the implications of shadow prices as explained in the correct answer.

Explanation

The correct answer highlights the importance of shadow prices in determining the maximum premium for a scarce resource and the necessity of considering them carefully. The incorrect answers provide false statements that do not align with the implications of shadow prices as explained in the correct answer.

5. What is slack and why is it important?

Slack is the amount by which a resource is over-utilised. It is important to avoid wasting resources.

Slack is the amount by which a resource matches its utilization target. It is important for maintaining resource efficiency.

Slack refers to under-utilisation of resources, not overutilisation. It is important because unused resources can be redirected for alternative uses, increasing overall efficiency.

Explanation

Slack refers to under-utilisation of resources, not overutilisation. It is important because unused resources can be redirected for alternative uses, increasing overall efficiency.