Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A baker has kg of flour and kg of sugar. A tray of cookies uses kg of flour and kg of sugar and earns a profit of rupees. A tray of cakes uses kg of flour and kg of sugar and earns a profit of rupees. Find how many trays of each she should bake to earn the most, and the profit. Use the corners of the region, or linprog as a check.
Name the unknowns and with their units. Write the objective, such as the profit . Write one inequality for each limit, and add and . Find the corners of the feasible region, work out at each, and choose the best. Say the plan and the value in the words of the story.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The model. Let be the trays of cookies and the trays of cakes. Maximise rupees subject to , , and .
Step 2. The corners. Subtracting the second equation from the first gives , so , and then . The other corners are , and .
Step 3. The profit. At , . At , . At , . At , .
Step 4. Say it. Bake trays of cookies and trays of cakes. The profit is rupees.
Check. Flour used is kg and sugar used is kg. Both stocks are used completely.
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