Writing Systems of Inequalities

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What is a system of inequalities?

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A system of inequalities is a set of two or more inequalities that share the same variables. The solution to the system is the set of all points that satisfy all inequalities in the system.

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How do you represent a maximum constraint in a system of inequalities?

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It represents that the total number of reserved tickets (r) and general admission tickets (g) sold cannot exceed 1200.

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It represents that the total earnings from two jobs, where x is hours worked at $5/hour and y is hours worked at $7/hour, must be at least $65.

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How do you express a minimum requirement in a system of inequalities?

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It indicates that the total hours worked mowing lawns (m) and planting gardens (g) cannot exceed 40 hours.

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It represents that the total cost of vegetarian dinners (x) at $5 each and meat-based dinners (y) at $6 each cannot exceed $70.

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It signifies that the total number of CFL (C) and LED (L) lightbulbs purchased must equal 800.

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How do you determine the feasible region for a system of inequalities?

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The feasible region is determined by graphing each inequality on a coordinate plane and identifying the area where all inequalities overlap.

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What is the role of the objective function in a system of inequalities?

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The objective function is the equation that needs to be maximized or minimized, often representing profit, cost, or other quantities of interest.