The owner of a jewelry store has to decide how to allocate a budget of $$660000.$ He notices that the earnings of the company depend on investment in inventory $x_1($in thousands of dollars$)$ and expenditure $x_2$ on advertising $($in thousands of dollars$)$ according to the function $f(x,y)=6x_1^{\frac{2}{3}}{x}_2^{\frac{1}{3}}.$

How should the owner allocate the $$660000$ between inventory and advertising to maximize his profit?

The owner should spend $ on the inventory and $ on the advertising.