Final answer:
To represent a budget scenario involving bratwursts and hamburgers, a system of inequalities can be set up based on cost and quantity constraints. The feasible region can be visualized by graphing the inequalities. The system of inequalities would involve cost constraints, quantity constraints, and non-negative constraints for the number of bratwursts and hamburgers purchased.
Step-by-step explanation:
The system of inequalities that represents a budget scenario involving bratwursts and hamburgers would involve defining the variables, setting up the inequalities based on the cost constraints, and graphing the inequalities to find the feasible region. Let's say the cost of a bratwurst is $5 and the cost of a hamburger is $3. If the budget allows for a maximum of $30 and a maximum of 8 items purchased, the inequalities would be:
- 5x + 3y <= 30 (cost constraint)
- x + y <= 8 (quantity constraint)
- x >= 0 (non-negative constraint for bratwursts)
- y >= 0 (non-negative constraint for hamburgers)
Graphing these inequalities on a coordinate plane would help visualize the feasible region, representing the combinations of bratwursts and hamburgers that fit within the budget constraints.
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