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Systems of Linear Inequalities

1) What conditions need to be satisfied for a solution of a system of linear inequalities to have it's solution in the first quadrant? Create an example of such a system.

2) Can you give a real world example when the solution of a system of inequalities must be in the first quadrant?

3) Suppose, wheat and sugar are two basic ingredients necessary to bake two items: a loaf of bread and a muffin. A baker has 25 pounds of wheat and 5 pounds of sugar. To bake each loaf of bread, the baker needs to use 1.3 pounds of wheat and .5 pound of sugar. To bake each muffin, the baker need needs .4 pound of wheat and .16 pound of sugar.

Can you set up the inequalities representing the baker's possible choices for baking the number of loaves of bread and muffins to use up his available resources (wheat and sugar)?? If each loaf of bread is sold for $2.50 and each muffin is sold for $1.15, can you define an equation to represent the baker's profit function?

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Solution Preview

1) What conditions need to be satisfied for a solution of a system of linear inequalities to have its solution in the first quadrant? Create an example of such a system.

For a system of linear inequalities to have a solution in the first quadrant, it is required that the variables involved in the setup should all be positive. An example is:
x + y >= 5
xy >= 6

2) Can you give a real world example when the solution of a system of inequalities must be in the first quadrant?
A company makes two ...

Solution Summary

Systems of Linear Inequalities in real life are discussed.

$2.19