Problem: Minimize the objective function: C = 1000x + 1500y

The graph of the feasible region is show below.

graph with one line intersecting points at (35,0) and (5,10) and another line intersecting at points (5,10) and (0,25) and a third line interecting at (40,0) and (0,40) with feasible region shaded

Remember, find the vertices of the feasible region and plug it into C. The smallest value you can get for C is the minimum value, and the x and y you plugged in are the other answers.

The minimum value of C is ___ and occurs when x = ____ and y = ____.

Answer: The minimum value of C is 20,000 and occurs when x = 5 and y = 10.

Problem: Minimize the objective function: R = 6x + 20y

The graph of the feasible region is show below.

graph with one line intersecting points at (30,0) and (10,40), and second line with points at (80,20) and a third line with points at (90,0) and (10,40) and the feasible region shaded

Remember, find the vertices of the feasible region and plug it into R. The largest value you can get for R is the maximum value, and the x and y you plugged in are the other answers.

The minimum value of R is ___ and occurs when x = ____ and y = ____.

Answer: The minimum value of C is 860 and occurs when x = 10 and y = 40.

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