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 zequals5xplus4​y? 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 zequals5xplus4​y? 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