Baking a tray of corn muffins takes 4 cups of milk and 3 cups of wheat flour. Baking a tray of bran muffins takes 2 cups of milk and 3 cups of wheat flour. A baker has 20 cups of milk and 18 cups of wheat flour. He makes $3 profit per tray of corn muffins and $2 profit per tray of bran muffins. How many trays of each type of muffin should the baker make to maximize his profit?

2 barn and 4 corn

Step-by-step explanation:

Here we have to pay attention to milk, because both recipes require the same amount of flour, 3 cups, so the flour will be used in equal amounts whatever the recipe we use. Given this, we can only bake 6 trays at most.

Can we bake 6 of barn? YES! Using all our flour and 6*2=12 cups of milk and getting 6 trays of barn muffins. This will give us $2 * 6 = $12. However we keep 8 cups of milk with not use, that could have been used to bake one of corn that are twice as profits as barn. What happens if we replace one of the 6 barn trays by one of corn?

This way we will have 5 of barn and 1 of corn and we will be using 10 + 4 = 14 cups of milk. Our profits will be: $2*5 + $3*1 = $13. This will improve our income!

Lets replace another barn by one of corn. This way we have 4 of barn and 2 of corn: $2*4 + $3*2 = $14. Again, more income!

Lets replace another and have 3 barn and 3 corn: $2*3 + $3*3 = $15. And we can bake them, as they need 2*3 = 6 cups for barn and 4*3=12 cups of milk for corn.

If we replace another we will have 2 of barn and 4 of corn. Our income will be: $2*2 + $3*4 = $16. This implies using 4 cups of mil for barn and 16 cups of mil for corn. So, we use all of our milk.

Any change in the distribution of barn and corn will, even impossible to bake as there will not be more ingredients or less profit