Find the minimum cost of producing 60000 units of a product, where x is the number of units of labor, at $99 per unit, and y is the number of units of capital expended, at $84 per unit. And determine how many units of labor and how many units of capital a company should use. Where the production level is given by P(x, y) = 100x^0.25 y^0.75

The minimum cost of producing 60000 units of a product is $105867

Step-by-step explanation:

Since x is the number of units of labor, at $99 per unit, and y is the number of units of capital expended, at $84 per unit, The cost C(x,y) is given by:

For the minimum cost:

Using the langrage multiplier,

Dividing both equation 1 and 2

Substituting in , we get:

labor units

Substituting  labor units in , we get

labor unit

The minimum cost of producing 60000 units of a product is $105867

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