An objective function and a system of linear inequalities representing constraints are shown on the right.**Objective function:** $ z = x + 6y $**Constraints:** $ x \geq 0, \, y \geq 0 $ $ x + y \geq 1 $ $ 3x + 4y \leq 12 $ $ 4x + 3y \leq 12 $---**a.** Graph the system of inequalities representing the constraints. Choose the correct graph below.- **Option A:** Incorrect graph - **Option B:** Incorrect graph- **Option C:** Correct graph**Explanation of Graph C:** The graph displays a shaded feasible region that satisfies all given constraints. The x-axis ranges from -2 to 12, and the y-axis ranges from -2 to 12. The boundaries of the shaded region correspond to the constraints. The lines are drawn for each inequality constraint, with the shaded area indicating the feasible solutions.---**b.** Find the value of the objective function at each corner of the graphed region.The values of the objective function are $ \underline{\quad} $. (Type an integer or a fraction. Use a comma to separate answers as needed.)

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Description: An objective function and a system of linear inequalities representing constraints are shown on the right.**Objective function:** $ z = x + 6y $**Constraints:** $ x \geq 0, \, y \geq 0 $ $ x + y \geq 1 $ $ 3x + 4y \leq 12 $ \( 4x + 3y \

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An objective function and a system of linear Objective function z=x+6y inequalities representing constraints are shown on the right. x20, y20 x+y21 Constraints 3x + 4y s 12 4x + 3y s 12

Algebra and Trigonometry (6th Edition)

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Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

An objective function and a system of linear inequalities representing constraints are shown on the right.

**Objective function:**
$ z = x + 6y $

**Constraints:**
$ x \geq 0, \, y \geq 0 $
$ x + y \geq 1 $
$ 3x + 4y \leq 12 $
$ 4x + 3y \leq 12 $

---

**a.** Graph the system of inequalities representing the constraints. Choose the correct graph below.

- **Option A:** Incorrect graph
- **Option B:** Incorrect graph
- **Option C:** Correct graph

**Explanation of Graph C:**
The graph displays a shaded feasible region that satisfies all given constraints. The x-axis ranges from -2 to 12, and the y-axis ranges from -2 to 12. The boundaries of the shaded region correspond to the constraints. The lines are drawn for each inequality constraint, with the shaded area indicating the feasible solutions.

---

**b.** Find the value of the objective function at each corner of the graphed region.

The values of the objective function are $ \underline{\quad} $.
(Type an integer or a fraction. Use a comma to separate answers as needed.)

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