A Company Manufactures a Product Using X, Y and Z $Q = 60 x ^ { \frac { 1 } { 3 } } y ^ { \frac { 1 } { 4 } } z ^ { \frac { 2 } { 5 } }$

question 77

Essay

A company manufactures a product using x, y and z units of three different raw materials.The quantity produced is given by The production is described by the function $Q = 60 x ^ { \frac { 1 } { 3 } } y ^ { \frac { 1 } { 4 } } z ^ { \frac { 2 } { 5 } }$ .Suppose the cost of the materials per unit is $20, $15 and $24 respectively.
(a)Find the cheapest way to produce 6300 units of the product.
(b)Find the value of $\lambda$ in $\nabla f = \lambda \nabla Q$ and interpret this value.

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Definitions:

Wampanoag Chief

A leader of the Wampanoag, a Native American tribe from the northeastern United States, known historically for their involvement in early interactions with European settlers, including the first Thanksgiving.

Imported Goods

Items brought into a country from abroad for sale or trade.

European Colonies

were territories outside of Europe that were controlled and exploited by European powers from the 16th to the 20th centuries for economic, military, and strategic advantages.

Jesuit Influence

The impact and contributions of the Jesuit order, a Catholic religious society, in various fields such as education, missionary work, and scholarly research globally.