Solve: "Baking a tray of corn muffins takes 4 cups of milk and 3 cups of wheat flower.Baking a tray of bran muffins takes 2 cups of milk and 3 cups...

We know from enunciation that baking a tray of corn
muffins takes 4 cups of milk and 3 cups of wheat flour and the resulted profit is $3.
And baking a tray of bran muffins takes 2 cups of milk and 3 cups of wheat flour and
the profit is $2.

From the amount of 16 cups of milk the
baker can make 4 trays of corn muffins or 6 trays of bran
muffins.

From the amount of 15 cups of wheat flour the
baker can bake the same number of trays: 5 trays of corn muffins or 5 trays of bran
muffins.

We'll impose the following
constraints:

- for baking x trays of corn muffin, the profi
made is: $3x

- for baking y trays of bran muffin, the
profit made is $2y

- 3x + 2y < 15 (the smaller
amount of wheat flour)

 We'll express y with respect to x.
For this reason, we'll subtract 3x both sides:

2y <
15 - 3x

We'll divide by 2:

y
< (15 - 3x)/2

For x =
1

y < (15 -
3)/2

y< 6

The profit
made is:

3x + 2y = 3*1 + 2*6 = 3 + 12 =
$15

For x = 2

y < (15 -
6)/2

y < 9/2

y <
4.5

Since y is integer, then y = 4 <
4.5

The profit made is:

3x +
2y = 3*2 + 2*4 = 6 + 8 = $14

For x =
3

y < (15 - 9)/2

y
< 6/2

y < 3

The
profit made is:

3x + 2y = 3*3 + 2*3 = 9 + 6 =
$15

For x = 4:

y < (15
- 12)/2

y < 3/2

y
< 1.5

Since y is integer, then y = 1 <
1.5

The profit made is:

3x +
2y = 3*4 + 2*1 = 12 + 2 = $14

We notice that
the maximum profit is $15.

We
also notice that the baker can make maximum profit of $15, by baking 1 tray of corn
muffins and 6 trays of bran
muffins.

The baker can make
maximum profit of $15, by baking 3 trays of corn muffins and 3 trays of bran
muffins.