Questions: Homework: Ch 5 sec 5.3 Question 2, 5.3.9 HW Score: 10%, 1 of 10 points Part 1 of 3 Points: 0 of 1 Graph the constant-profit lines for the objective function P=x+y through (2,2) and also through (4,4). Use a straightedge to identify the corner point where the maximum profit occurs. Confirm your answer by constructing a corner point table. Which graph below has the correct constant-profit lines?

Homework: Ch 5 sec 5.3 Question 2, 5.3.9 HW Score: 10%, 1 of 10 points Part 1 of 3 Points: 0 of 1 Graph the constant-profit lines for the objective function P=x+y through (2,2) and also through (4,4). Use a straightedge to identify the corner point where the maximum profit occurs. Confirm your answer by constructing a corner point table. Which graph below has the correct constant-profit lines?
Transcript text: Homework: Ch 5 sec 5.3 Question 2, 5.3.9 HW Score: $10 \%, 1$ of 10 points Part 1 of 3 Points: 0 of 1 Save Question list Question 1 Question 2 Question 3 Question 4 Question 5 Graph the constant-profit lines for the objective function $\mathrm{P}=\mathrm{x}+\mathrm{y}$ through $(2,2)$ and also through $(4,4)$. Use a straightedge to identify the corner point where the maximum profit occurs. Confirm your answer by constructing a corner point table. Which graph below has the correct constant-profit lines? A. B. $\square$ c. D. Clear all Check answer
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Solution

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Solution Steps

Step 1: Understand the Objective Function and Constraints

The objective function given is \( P = x + y \). The constraints are the lines passing through points (2,2) and (4,4).

Step 2: Identify the Feasible Region

The feasible region is the area bounded by the lines and the axes. The vertices of the feasible region are given as (0,0), (2,2), (4,4), and (13,0).

Step 3: Evaluate the Objective Function at Each Vertex

Calculate the value of \( P = x + y \) at each vertex:

  • At (0,0): \( P = 0 + 0 = 0 \)
  • At (2,2): \( P = 2 + 2 = 4 \)
  • At (4,4): \( P = 4 + 4 = 8 \)
  • At (13,0): \( P = 13 + 0 = 13 \)

Final Answer

The maximum profit occurs at the vertex (13,0) with a value of \( P = 13 \). The correct graph with the constant-profit lines is option D.

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