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The x and y that minimize the function is the point of intersection of the boundary lines of the two first equations.
x=3 and y=6
(I): LHS−4x=RHS−4x
(I): LHS/3=RHS/3
(II): LHS−x=RHS−x
(II): LHS/3=RHS/3
(II): ca⋅b=ca⋅b
Next, we have to set the calculator to account for the inequality. Place the cursor before Y and scroll by pushing ENTER. We will select the icon that displays a black triangle pointing up and to the right. This tells the calculator that we are dealing with a ≥ inequality.
With the inequalities entered in the calculator, we can graph them by pushing GRAPH. Before we do that let's limit the window to the first quadrant, as we have already established that we are interested in this area only.
The objective function is minimized where the boundary lines of the two first inequalities intersect. We can use the calculator to find this point of intersection. To do this, push CALC (2nd+TRACE) and choose the fifth option in the list, intersect.
Now we must provide the calculator with some guesses as to where the intersection occurs.
The solution is x=3 and y=6. These values minimize the objective function.