Math Problem Statement
The graph to the right shows a region of feasible solutions. Use this region to find maximum and minimum values of the given objective functions, and the locations of these values on the graph. (a) zequals5xplus4y (b) zequalsxplus2y Question content area bottom left Part 1 (a) What is the maximum of zequals5xplus4y? Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. A. The maximum value of the objective function zequals5xplus4y is 47 and is located only at the point(s) left parenthesis 7 comma 3 right parenthesis. (Type exact answers. Use a comma to separate answers as needed.) Your answer is not correct.B. The maximum value of the objective function zequals5xplus4y is enter your response here. It is located at the points enter your response here and at all points on the line segment connecting them. (Type exact answers. Use a comma to separate answers as needed.) C. The maximum does not exist. Part 2 What is the minimum of zequals5xplus4y? Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. A. The minimum value of the objective function zequals5xplus4y is enter your response here and is located only at the point(s) enter your response here. (Type exact answers. Use a comma to separate answers as needed.) B. The minimum value of the objective function zequals5xplus4y is enter your response here. It is located at the points enter your response here and at all points on the line segment connecting them. (Type exact answers. Use a comma to separate answers as needed.) C. The minimum does not exist.
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Programming
Optimization
Objective Functions
Feasible Region
Formulas
z = 5x + 4y
z = x + 2y
Theorems
Fundamental Theorem of Linear Programming
Suitable Grade Level
Grades 10-12
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