Question 317284: We have sugar and wheat as the two basic ingredients to bake two items. a loaf of bread and a muffin. we have 25lbs of wheat and 5 lbs sugar. To bake each loaf of bread it takes 1.3 lbs of wheat and .05 lbs of sugar. To bake each muffin it takes 0.4 lbs of wheat and 0.16lbs of sugar.How many loaves of bread and how many muffins can you make?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
You can't answer that question with a specific answer.
Let  represent the number of loaves of bread
Let  represent the number of muffins
You need to define an area of feasibility on the coordinate plane bounded by the following relationships:
because  is the amount of wheat you use for loaves of bread and muffins AND that cannot exceed the available amount of wheat. Likewise, to account for the constraint on the amount of sugar:
Now, since you can't make a negative number of loaves of bread or a negative number of muffins:
Also, because it would be silly to make fractional parts of loaves of bread or fractional parts of muffins, the solution set for this problem consists of ordered pairs, ) where  and 
From a practical point of view, what you need to do is to graph the boundaries of the two resource constraint inequalities and then the feasible area is the resulting quadrilateral bounded by the two boundary lines and the two coordinate axes. Any ordered pair with integer coefficients inside of or on the boundary of that area is a feasible solution.
So, below the green line, to the left of the red line, to the right of the  -axis, and above the  -axis -- only where grid lines cross.
John
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