To solve this problem, we must first understand the expression of z, and my method is to use vectors.

Z = (modulus length of OP vector) × (cosine value of included angle between vector OA and OP)

Z = (modular length of OP vector) × (quantitative product of vectors OA and OP)/(modular length product of vectors OA and OP)

Simplified z=(3x+ radical number 3y)/(2* radical number 3)

Then it can be solved by linear programming.