Part A – Patches’ Cat Food

Patches is a cat who eats cat food for breakfast. Patches requires a breakfast diet that includes at least 40g of protein, at least 90g of iron but no more than 144g of carbs a week.

His two favourite brands are Kitty Kibble and Cat Snack. Kitty Kibble contains 1g of protein, 11g of iron and 6g of carbohydrates per box. Cat Snack contain 5g of protein, 5g of iron and 6g of carbs per box.

Kitty Kibble costs $4 a box, Cat Snack costs $2 a box.

Patches’ owner wants to minimise how much money they spend on cereal while meeting Patches’ dietary requirements.

1. Construct a table showing:

• the number of the elements required for each item

• the amount of each element available or the minimum requirements of each element.

2. State the objective function and determine the constraints for each element.

3. Produce a labelled graph showing the feasible region.

4. Find the optimal solution by considering the feasible points.

5. Determine the wastage or oversupply of elements for the optimal solution.

6. Now investigate changes to the original scenario such as:

• the impact on the optimal value when the objective function is changed

• the impact on the optimal value, and wastage and oversupply, when changes are made to the original constraints by:

o changing the available amounts of minimal requirements

o changing the number of elements or items required

o adding a further constraint (such as a time limit).

Part B – Create a scenario

You need to select a scenario to investigate using linear programming techniques.

The problem that you choose needs to investigate the optimal value for a combination of two items. The optimal value can be a minimum or maximum value. The two items need to have between 3 and 5 elements required.

1. Construct a table showing:

• the number of the elements required for each item

• the amount of each element available or the minimum requirements of each element.

2. State the objective function and determine the constraints for each element.

3. Produce a labelled graph showing the feasible region.

4. Find the optimal solution by considering the feasible points.

5. Determine the wastage or oversupply of elements for the optimal solution.

6. Now investigate changes to the original scenario such as:

• the impact on the optimal value when the objective function is changed

• the impact on the optimal value, and wastage and oversupply, when changes are made to the original constraints by:

o changing the available amounts of minimal requirements

o changing the number of elements or items required

o adding a further constraint (such as a time limit).

Analysis / Conclusion

Critically analyse your results, considering:

• a comparison of the different scenarios investigated

• the optimal solution obtained

• the reasonableness of the optimal solution

• the best scenario for the efficient completion of the task

• the limitations of the model used.

Scenario ideas

Students may select an activity that is part of the context being studied, for example:

• determining a combination of two food items for a week when there are minimum or maximum dietary requirements

• producing two different food products for sale

• constructing two different products for sale (consider woodwork/metalwork or craft items)

• providing a car cleaning service with two sized vehicles.

• creating two gift basket combinations with a range of products

Possible extensions:

• You may like to consider integer/non-integer solutions if the context is appropriate.

• You may like to consider multiple optimal solutions if they occur.

The investigation report should be a maximum of 12 single-sided A4 pages if written, or the equivalent in multimodal form.

Report Format

The report may take a variety of forms, but would usually include the following:

– an outline of the problem and context

– the method required to find a solution, in terms of the mathematical model or strategy used

– the application of the mathematical model or strategy, including

o relevant data and/or information

o mathematical calculations and results using appropriate representations

o discussion and interpretation of results, including consideration of the reasonableness and limitations of the results

– the results and conclusions in the context of the problem.

A bibliography and appendices, as appropriate, may be used.

The format of an investigation report may be written or multimodal

The post Part A – Patches’ Cat Food Patches is a cat who eats cat food for breakfast. Patches requires a breakfast diet that includes at least 40g of protein, at least 90g of iron but no more than 144g of carbs a week. His two favourite brands are Kitty Kibble and Cat Snack. Kitty Kibble contains 1g of protein, 11g of iron and 6g of carbohydrates per box. Cat Snack contain 5g of protein, 5g of iron and 6g of carbs per box. Kitty Kibble costs $4 a box, Cat Snack costs $2 a box. Patches’ owner wants to minimise how much money they spend on cereal while meeting Patches’ dietary requirements. 1. Construct a table showing: • the number of the elements requir appeared first on My blog.