# An objective function and a system of linear inequalities representing constraints are given. Complete parts​ (a) through​ (c). Objective Functionzequals=3 x plus y3x+yConstraintsleft brace Start 3 By 1 Matrix 1st Row 1st Column x less than or equals 4 2nd Row 1st Column y greater than or equals 2 3rd Row 1st Column 4 x minus y greater than or equals minus 2 EndMatrixx≤4y≥24x−y≥−2a. Graph the system of inequalities representing the constraints.Graph each inequality individually and then use those results to graph the system. Combining these three inequalities results in the graph shown to the right.b.Find the value of the objective function at each corner of the graphed region. Now calculate the value.c. Use the values in part​ (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

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An objective function and a system of linear inequalities representing constraints are given. Complete parts​ (a) through​ (c).

Objective Function
zequals=3 x plus y3x+y
Constraints
left brace Start 3 By 1 Matrix 1st Row 1st Column x less than or equals 4 2nd Row 1st Column y greater than or equals 2 3rd Row 1st Column 4 x minus y greater than or equals minus 2 EndMatrix
 x≤4 y≥2 4x−y≥−2
a. Graph the system of inequalities representing the constraints.
Graph each inequality individually and then use those results to graph the system. Combining these three inequalities results in the graph shown to the right.
b.Find the value of the objective function at each corner of the graphed region. Now calculate the value.
c. Use the values in part​ (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.
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Step 1

a

It is given that the objective function is z = 3x + y.

Constraints are:

Step 2 Step 3 ...

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