Let z = ax + by be an objective function that depends on x and y. Furthermore, z is subject to a number of constraints on x and y. If a maximum or minimum value of z exists, it can be determined as follows: 1. Graph the system of inequalities representing the constraints. 2. Find the value of the objective function at each corner, or vertex, of the graphed region. The maximum and minimum of the objective function occur at one or more of the corner points.
Let z = ax + by be an objective function that depends on x and y. Furthermore, z is subject to a number of constraints on x and y. If a maximum or minimum value of z exists, it can be determined as follows: 1. Graph the system of inequalities representing the constraints. 2. Find the value of the objective function at each corner, or vertex, of the graphed region. The maximum and minimum of the objective function occur at one or more of the corner points.
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
Problem 10CT: Sketch the region corresponding to the system of constraints. Then find the minimum and maximum...
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Use the two steps for solving a linear programming problem given to solve:You are about to take a test that contains computation problems worth 6 points each and word problems worth 10 points each. You can do a computation problem in 2 minutes and a word problem in 4 minutes. You have 40 minutes to take the test and may answer no more than 12 problems. Assuming you answer all the problems attempted correctly, how many of each type of problem must you answer to maximize your score? What is the maximum score?
Transcribed Image Text:Let z = ax + by be an objective function that depends on x and y. Furthermore,
z is subject to a number of constraints on x and y. If a maximum or minimum
value of z exists, it can be determined as follows:
1. Graph the system of inequalities representing the constraints.
2. Find the value of the objective function at each corner, or vertex, of the
graphed region. The maximum and minimum of the objective function
occur at one or more of the corner points.
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