find the ordered pair where the maximum value occurs for the equation .. below

Question

c=12 x-4y given the following constraints

y greater than or equal to 4

x greater than or equal to 1

x+2y less than or equal to 16

y-x less than or equal to 5

Answer 1

I can't put a graph in here, so I'll just describe the steps you'll need to complete the problem.

1. Graph the constraints (the y >= 4, x >=1, x+2y <= 16, and y-x <=5). You can use your graphing calculator if you'd like.

2. Find the coordinates of each vertex (the points at which the constraint lines meet, the corners of the boundary of your shaded area).

3. Evaluate your objective function (c = 12x - 4y) for each vertex (plug in the x and y coordinate of each pair and solve for c)

4. Look for the largest value of c from your list of solved equations. The corresponding vertex is your answer.