An agricultural company has 80 tons of Type I fertilizer and 120 tons of Type II fertilizer. The company mixes both types of fertilizer into 3 raw material blends. Blend X requires 3 parts of Type I and 1 part of Type II. Blend Y requires 1 part of Type I and 4 parts of Type II. Blend Z requires half a part of Type I and 2 parts of Type II. Blend X is sold at $2000 per ton, Blend Y at $1500 per ton, and Blend Z is sold at $2500 per ton. Use the following decision variables:

x: number of tons to mix of Blend X y: number of tons to mix of Blend Y z: number of tons to mix of Blend Z

to formulate the company's mathematical optimization problem.