I have a linear programming word problem that I think I have almost solved but I could use some help. The question is: solve the following optimization problem and be sure to include the statement of the optimization problem and also graph of the feasible set.

Tim has joined a block building contest. A diamond shape requires 4 yellow blocks and 5 purple blocks to build. A heart shape requires 14 red blocks and 11 blue blocks to build. Tim's been given a supply of 250 yellow blocks and 180 purple blocks.

If a diamond shape is worth 3 points and a heart shape is worth 8 points, how many shapes of each type should Tim build to maximize the points.

This is what I have come up with so far.

Let the diamond shaped blocks be X and let the heart shaped blocks be Y

Yellow Purple

diamond shape 4 5 X

heart shape 14 11 Y

X>=0. Y>=0 My statement of optimization would be P= 5X + 3Y subject to

4X + 14Y <=250

5X + 11Y <= 180

After this I am a little stuck I know I have to graph the equations and get the corner points. Am I on the right track with the equations I have come up with to determine the maximum points per shapes?