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

question 70

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?

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Definitions:

Copper

A reddish-brown metal with high thermal and electrical conductivity, widely used in electrical wiring and coinage.

Vitamin E

A group of fat-soluble compounds with distinct antioxidant properties that are essential for health, particularly in protecting cell membranes from damage.

Green Leafy Vegetables

A category of vegetables with green leaves, rich in vitamins, minerals, and fiber, including spinach, kale, and lettuce; vital for a healthy diet.

Vitamin A

A fat-soluble vitamin important for vision, the immune system, and skin health.