Question: The manufacture of 1 unit of a product has a cost (in dollars) given by
C(x, y, z) = 10 + 8x + 3y + z
where x is the cost of 1 pound of one raw material, y is the cost of 1 pound of a second raw material, and z is the cost of 1 work-hour of labor.
(a) If the cost of the first raw material is $16 per pound, the cost of the second raw material is $8 per pound, and labor costs $18 per work-hour, what will it cost to produce 1 unit of the product?
(b) Find and interpret the partial derivative of C with respect to x.