Limiting Factor Decisions

Question 1

When dealing with limiting factors, what is the rule in the following scenarios:
1. Resources are unlimited.
2. A factor of production is limited.

Answer 1

When resources are unlimited - make all those products which give “positive contribution”, up to maximum demand.

Where a factor of production is limited - contribution and profit will be maximised by concentration production on the product(s) which make(s) best use of the scarce resource, up to maximum demand.

Question 2

List the five steps used in deciding which products to produce to maximise contribution and therefore profit, where one of the factors of production is limited.

Answer 2

1. Identify the limiting factor.
2. Calculate contribution per unit of each product.
3. Calculate contribution per unit of limiting factor for each product:
   Contribution per unit / unit of scarce resource used
4. Rank the products according to the contribution per unit of limiting factor.
5. Concentrate production in those products with the highest contribution per unit of limiting factor.

Question 3

What are some of the limitations of the key factor analysis approach to decision making?

Answer 3

1. It assumes a single objective of contribution/profit maximisation.
2. It assumes constant variable cost per unit and constant fixed costs; this may only hold true over a narrow range of activity (e.g. discounts may apply to materials or sales for larger quantities).
3. It deals with only one scarce resource; if there is more than one, linear programming must be used.
4. It applies only to situations in which capacity constraints cannot be removed in the short term.

Question 4

What is the shadow (dual) price?

Answer 4

Shadow price is the additional contribution that would be generated if one more unit of the resource were to become available.

The shadow price represents the maximum premium over the normal price the company would be prepared to pay for each additional unit.

Question 5

In make v buy decisions where the cost of making components in house is cheaper than outsourcing but the company can’t produce all items, how would the business decide which items to make?

Answer 5

The business should make those components or products where the biggest savings can be made and outsource the remainder. To do this, calculate the:
savings per unit of scarce resource = (buy-in price - variable cost to make)/number of units of scarce resource used per unit.

Question 6

In make v buy situations, how is the shadow price calculated?

Answer 6

The shadow price is the savings per unit of scarce resource.

Question 7

List the four steps in graphing a linear programming model.

Answer 7

1. Define unknowns.
2. Formulate the objective function, either to maximise contribution or minimise cost.
3. Express constraints in terms of inequalities.
4. Plot all constraints on a graph and identify the feasible region.