Find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints. (You should graph the feasible solutions on the grid below before you attempt to find the minimum and maximum values.)

Question

Quizplus · Accepted Answer

To find the minimum and maximum values of the objective function, we need to evaluate the function at each corner point of the feasible region. From the graph, we can see that there are four corner points: (0,0), (0,3), (2,1), and (3,0).

At (0,0), the objective function evaluates to f(0,0) = 0.
At (0,3), the objective function evaluates to f(0,3) = 48.
At (2,1), the objective function evaluates to f(2,1) = 36.
At (3,0), the objective function evaluates to f(3,0) = 33.

Therefore, the minimum value of the objective function is 0 and occurs at (0,0), while the maximum value is 48 and occurs at (0,3). The only choice that includes both the minimum and maximum values is D.

Find the Minimum and Maximum Values of the Objective Function