The maximum value of the objective function is 1 if the subject to the constraints x ≥ 0, − x + y ≥ 0, and y ≤ 2.
What is inequality?
It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
The objective function f(x, y) = x − y + 1
The subject to constraints:
x ≥ 0, − x + y ≥ 0, and y ≤ 2
First, plot all the inequality, the coordinate plane:
The intersection region is shown in the graph.
The objective function:
f(x, y) = x − y + 1
Checking boundary points:
Plug x = 0 and y = 2
f(0, 2) = 0 − 2 + 1
f(0, 2) = -1
Plug x = 2 and y = 2
f(2, 2) = 2 − 2 + 1
f(2, 2) = 1
Plug x = 0 and y = 0
f(0, 0) = 0 − 0 + 1
f(0, 0) = 1
Plug x = 1 and y = 1
f(1, 1) = 1 − 1 + 1
f(1, 1) = 1
Plug x = 0 and y = 1
f(0, 1) = 0 − 1 + 1
f(0, 1) = 0
Plug x = 1 and y = 2
f(1, 2) = 1 − 2 + 1
f(1, 2) = 0
Thus, the maximum value of the objective function is 1 if the subject to the constraints x ≥ 0, − x + y ≥ 0, and y ≤ 2.
Learn more about the inequality here:
brainly.com/question/19491153
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