Difficult maths problem

How would I go about answering the following problem:

“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.”

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.

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.

sorry teh editing didnt copy and paste through i deleted it.

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.

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