Your club has decided to volunteer to clean up your school grounds and plant some bushes and trees. You learn that you need to spend $18 for each bush and $22 for each tree. You realize that you cannot plant more than 20 trees. Your school says that you should plant at least a total of 12 plants but no more than 40. The number of trees must be at least 1/3 the number of bushes.

Under the given conditions, what is the minimum amount you could spend on the plants?

Formulate a linear programming model for this problem. Make sure to explain in words what your decision variables represent. (Do not solve, please just type your mathematical formulation here)