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

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.