The Owner of a Jewelry Store Has to Decide How $f ( x , y ) = 6 x _ { 1 } ^ { 2 / 3 } x _ { 2 } ^ { 1 / 3 }$

Essay

The owner of a jewelry store has to decide how to allocate a budget of $540,000.He notices that the earnings of the company depend on investment in inventory x₁ (in thousands of dollars)and expenditure x₂ on advertising (in thousands of dollars)according to the function $f ( x , y ) = 6 x _ { 1 } ^ { 2 / 3 } x _ { 2 } ^ { 1 / 3 }$ How should the owner allocate the $540,000 between inventory and advertising to maximize his profit?