SOLUTION: Catherine is making chocolate tea bread and a special oatmeal bread to sell at a bake sale. A batch of chocolate tea bread requires 2 eggs and 2 cups of flour. The oatmeal bread

Question 814098: Catherine is making chocolate tea bread and a special oatmeal bread to sell at a bake sale. A batch of chocolate tea bread requires 2 eggs and 2 cups of flour. The oatmeal bread requires 3 cups of flour and 1 egg. Catherine has 12 cups of flour and 8 eggs on hand. She makes a profit of $2 on both kinds of bread. Write a set of constraints that could be used to graph the feasible region.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
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.

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.

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.

Now for the constraints:
since we cannot make a negative number of batches
since we cannot make a negative number of batches
since we cannot use more eggs than we have
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.)

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.
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