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# The bakery problem

Learn about technology-assisted decision-making. Discover techniques to optimize industry, health, and education

In the animation, we introduced you to the bakery problem.

## The bakery problem in detail

• The dough for each bread is a mixture of wholemeal flour, spelt flour and strong white bread flour but in different proportions.
• Each day in the bakery there is a fixed amount of wholemeal flour and white bread flour.
• A 1Kg loaf of Bread B sells for £3.00 , and a 1Kg loaf of Bread A sells for £1.50.

Here is the recipe for each type of bread:

Wholemeal flour Spelt flour Strong white flour
Bread A (1Kg) 0.2Kg 0.2Kg 0.6Kg
Bread B (1Kg) 0.5Kg 0.2Kg 0.3Kg
Total available 50Kg 30Kg 100Kg

## The problem

The bakery would like to know how much of Bread A and Bread B to make in order to maximise their turnover. Turnover is a financial measure that represents the total amount of sales generated by a business during a specific period of time. It is typically calculated by multiplying the number of units sold by the price of each unit.

For example, if a company sells 10,000 units of a product per year at a price of £50 per unit, its turnover would be £500,000 per year.

Turnover is an important metric for businesses because it provides insight into the company’s performance and can be used to evaluate its efficiency and profitability. A high turnover indicates that the business is selling a large volume of products. A low turnover may suggest that the company is not effectively managing its inventory (or stock) or that its pricing strategy is not competitive.

It’s important to note that turnover is different from profit. Profit represents the amount of money a business makes after deducting all of its expenses. A company can have a high turnover but low profit if its expenses are high or its profit margins are low. Conversely, a company can have a low turnover but high profit if it sells a smaller volume of products at a higher price point.

There are lots of solutions that are within the constraints of the bakery. One possible solution might be that the bakery makes 50kg of Bread A, and 30kg of Bread B. For these quantities of Bread A and Bread B we will need a certain amount of wholemeal flour, spelt flour and strong white flour.

Let’s work out how much of each type of flour this will require.

To work out the amount of wholemeal flour required we multiply the amount of wholemeal flour required to make 1Kg of Bread A by the number of kilograms of bread we wish to make.

So, to make 10 loaves of bread, we’ll need 50 x 0.2kg of wholemeal flour:

(50×0.2=10)

To work out the amount of Spelt flour required we multiply the amount of spelt flour required to make 1Kg of Bread A by the number of kilograms we wish to make.

(50×0.2=10)

To work out the amount of strong white flour required we multiply the amount of strong white flour required to make 1Kg of Bread A by the number of kilograms we wish to make.

(50×0.6=30)

To work out the amount of wholemeal flour required we multiply the amount of wholemeal flour required to make 1kg of Bread B by the number of kilograms we wish to make.

(30×0.5=15)

To work out the amount of spelt flour required we multiply the amount of spelt flour required to make 1Kg of Bread B by the number of kilograms we wish to make.

(30×0.2=6)

To work out the amount of strong white flour required we multiply the amount of strong flour required to make 1Kg of Bread B by the number of kilograms we wish to make.

(30×0.3=9)

This gives us the following:

Wholemeal flour Spelt flour Strong white flour
Bread A (50Kg) 10Kg 10Kg 30Kg
Bread B (30Kg) 15Kg 6Kg 9Kg
Total used 25Kg 16Kg 39Kg
Total available 50Kg 30Kg 100Kg
Used flour 25Kg 14Kg 61Kg

This would, assuming that all of the bread is sold, produce a turnover of £75 from bread A, £90 from bread B, for a total turnover of £165. Is this the maximum turnover the bakery can produce?

From the above table you can see that by making 50Kg of Bread A and 30Kg of Bread B the bakery will have 25Kg of unused wholemeal flour remaining, 14Kg of unused spelt flour remaining and 61Kg of unused strong white flour remaining. This is sufficient to make more bread of either type so it should be possible to find a better solution which increases the turnover of the bakery.

## Questions

Can you find different quantities of Bread A and Bread B which produces more turnover while staying within the constraints?
Can you find different quantities of Bread A and Bread B which produces less turnover while staying within the constraints?

Let’s move on to the next step to look at how to answer these questions.