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“James has recently opened a new bakery. He has 22.5kg of flour, 24kg of butter and 21kg of sugar available. The best selling items are shortbread and pancakes. Shortbreads need 120g of flour, 96g of butter and 132g of sugar for 16.
Pancakes need 240g of flour, 300g of butter and 180g of sugar for 24.
(He has plenty of the other ingredients needed.)

Shortbreads sell for £1.75 a pack of 4 and Pancakes for £1.95 a pack of 4. All are sold by the end of each day.
Recommend the number of shortbread and pancakes that should be baked and state the expected income.”
2. This looks like a linear programming problem. I assume you must have studied the topic, so start out by formulating an objective function and constraints.
3. (Original post by Billy_\1100)

“James has recently opened a new bakery. He has 22.5kg of flour, 24kg of butter and 21kg of sugar available. The best selling items are shortbread and pancakes. Shortbreads need 120g of flour, 96g of butter and 132g of sugar for 16.
Pancakes need 240g of flour, 300g of butter and 180g of sugar for 24.
(He has plenty of the other ingredients needed.)

Shortbreads sell for £1.75 a pack of 4 and Pancakes for £1.95 a pack of 4. All are sold by the end of each day.
Recommend the number of shortbread and pancakes that should be baked and state the expected income.”
sorry teh editing didnt copy and paste through i deleted it.
4. (Original post by TheMindGarage)
This looks like a linear programming problem. I assume you must have studied the topic, so start out by formulating an objective function and constraints.
I actually have no idea what that is. We haven’t learnt about that yet so there must be another way to do it. Any recommendations please?
5. (Original post by TheMindGarage)
This looks like a linear programming problem. I assume you must have studied the topic, so start out by formulating an objective function and constraints.
If you could give me an idea of how to start solving the program using linear programming, that would be great as we haven’t been taught about that yet.
6. (Original post by Alumna)
sorry teh editing didnt copy and paste through i deleted it.
Sorry, I don’t understand what you mean
7. (Original post by Billy_\1100)
If you could give me an idea of how to start solving the program using linear programming, that would be great as we haven’t been taught about that yet.
Start out by putting the recipies and prices in terms of a single shortbread or pancake. Define the objective function - this will be an expression for how much money you will make. Then formulate the constraints - these will be inequalities in terms of the number of shortbreads and pancakes made. One constraint for flour, one for sugar, one for butter.
8. (Original post by TheMindGarage)
Start out by putting the recipies and prices in terms of a single shortbread or pancake. Define the objective function - this will be an expression for how much money you will make. Then formulate the constraints - these will be inequalities in terms of the number of shortbreads and pancakes made. One constraint for flour, one for sugar, one for butter.
Okay, I have all the inequalities but how do I work out the maximum possible income from these inequalities? And thanks for your help so far
9. What level is this problem? Is a calculator allowed?
10. (Original post by Billy_\1100)
Okay, I have all the inequalities but how do I work out the maximum possible income from these inequalities? And thanks for your help so far
Put all the inequalities on a graph (they will all be straight lines) and shade any area that is unfeasible (ie it does not satisfy one or more of the inequalities). Then look at the vertices of the unshaded (feasible) region and calculate the objective function for each one. Pick the highest.
11. .....

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