Acca F5: Chapter 3 - Planning With Limiting Factors

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

Step 1: guess the bottleneck constraint. Step 2: assign equal resources to each product. Step 3: calculate the total revenue for each product. Step 4: rank products randomly. Step 5: allocate resources based on random ranking.

2 Planning with one limiting factor Step 1: identify the bottleneck constraint Step 2: calculate the contribution per unit for each product Step 3: calculate the contribution per unit of the bottleneck resource for each product Step 4: rank the products in order of the contribution per unit of the bottleneck resource Step 5: allocate resources using this ranking and answer the question

Step 1: estimate the total production capacity. Step 2: calculate the profit margin of each product. Step 3: identify the highest selling product. Step 4: rank products based on profit margin. Step 5: allocate resources based on the highest selling product.

Step 1: determine the least selling product. Step 2: calculate the fixed costs. Step 3: calculate the variable costs. Step 4: rank the products based on variable costs. Step 5: allocate resources based on fixed costs.

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 is slack and why is it important?

4 Shadow prices and slack 1) Slack is the amount by which a resource is under-utilised. It will occur when the optimum point does not fall on a given resource line. 2) Slack is important because unused resources can be put to another use, e.g. hired out to another manufacturer.

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 is the amount by which a resource is utilized at its maximum capacity. It is important for meeting production targets.

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.

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

4 Shadow prices and slack 1) It represents the maximum premium that the firm should be willing to pay for one extra unit of each constraint 2) The shadow price of a resource can be found by calculating the increase in value (usually extra contribution) which would be created by having available one additional unit of a limiting resource at its original cost. 3) Non-critical constraints will have zero shadow prices as slack exists already

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.

4. 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.

4 Shadow prices and slack Step 1: Take the equations of the straight lines that intersect at the optimal point. Add one unit to the constraint concerned, while leaving the other critical constraint unchanged. Step 2: Use simultaneous equations to derive a new optimal solution Step 3: Calculate the revised optimal contribution. The increase is the shadow price for the constraint under consideration.

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.

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

The feasible region remains unchanged regardless of changes in shadow prices

4 Shadow prices and slack - Management can use shadow prices as a measure of the maximum premium that they would be willing to pay for one more unit of the scarce resource - However, the shadow price should be considered carefully. For example, the shadow price of labour may be calculated as $20 per hour. However, it may be possible to negotiate a lower shadow price than this. - In addition, if more of the critical constraint is obtained, the constraint line will move outwards altering the shape of the feasible region. After a certain point there will be little point in buying more of the scarce resource since any non-critical constraints will become critical

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.