Question 814098
Note: The problem is not clear about the difference, if any, between a loaf of bread and a batch of bread. In the work below I have assumed that a loaf and a batch are the same thing.<br>
Let's define the following variables:
c = the number of batches of chocolate tea bread
m = the number of loaves of oatmeal bread ("O" is a bad name for a variable
Since each batch of chocolate bread requires 2 eggs:
2c = the number of eggs required for the chocolate bread
Since each batch of oatmeal bread requires 1 egg:
1m (or just m) = the number of eggs required for the oatmeal bread
And...
2c + m = the total number of eggs needed for both types of bread.<br>
Using similar logic on the flour we should find that:
2c + 3m = the total number of cups of flour needed for both types of bread.<br>
Now for the constraints:
{{{c >= 0}}} since we cannot make a negative number of batches
{{{m >= 0}}} since we cannot make a negative number of batches
{{{2c + m <= 8}}} since we cannot use more eggs than we have
{{{2c + 3m <= 12}}} since we cannot use more flour than we have
(We could also require that c and m be integers if we believe that fractional batches of bread are impossible.)<br>
P.S. The objective function would be, since $2 profit is made on each loaf of bread, would be:
P = 2c + 2m [or 2(c + m)]
where P is the total profit.