Gerber Mixed Cereal for Baby contains, in each serving, 60...

Gerber Mixed Cereal for Baby contains, in each serving, 60 calories, 11 grams of carbohydrates, and no vitamin C. Gerber Apple Banana Juice contains, in each serving, 60 calories, 15 grams of carbohydrates, and $120 \%$ of the U.S. Recommended Daily Allowance (RDA) of vitamin C for infants. "You want to provide your child with at least 120 calories, at least 26 grams of carbohydrates, and at least $50 \%$ of the U.S. RDA of vitamin $\mathrm{C}$ for infants. Draw the feasible region that shows the number of servings of cereal and number of servings of juice that you can give your child. Find the corner points of the region.

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Key Concepts

Corner Points (Extreme Points)

Corner points are the vertices at which the boundaries of the feasible region intersect. According to the fundamental property of linear programming, if an optimal solution exists, it is found at one of these corner points. Evaluating the objective function at these points enables the selection of the best possible solution under the given constraints.

Graphical Method in Linear Programming

This method involves plotting the linear inequalities on a coordinate system to visualize the feasible region. It is particularly useful for problems with two decision variables, as the feasible region and its boundary can be easily depicted, allowing for straightforward analysis of potential solutions.

Linear Inequalities

These are expressions that set limits on decision variables using inequality signs (such as ?, ?, >, or <). In optimization problems, they represent the constraints that restrict the values the variables can take, forming the boundaries of the solution space.

Feasible Region

This is the set of all points that satisfy the system of linear inequalities in a linear programming problem. Graphically, it is the intersection of the half-planes determined by each inequality, and it represents all the possible solutions that meet the problem's requirements.

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