The cost (in dollars) of manufacturing one item is given by E(x, y) = 40 + 2x +

Question

The cost (in dollars) of manufacturing one item is given by E(x, y) = 40 + 2x + 8y where x is the cost of 1 hour of labor and y is the cost of 1 pound of material. (a) If the hourly cost of labor is $18, and the material costs $8 per pound, what is the cost of manufacturing one of these items? (b) Find the partial derivative of C with respect to x. Interpret the partial derivative of C with respect to x O The cost (in dollars) of manufacturing one item will increase by $2 for a $1 increase in y if x is held constant. The cost (in dollars) of manufacturing one item will increase by $8 for a $1 increase in y if x is held constant. O The cost (in dollars) of manufacturing one item will increase by $40 for a $1 increase in x if y is held constant. O The cost (in dollars) of manufacturing one item will increase by $8 for a $1 increase in x if y is held constant O The cost (in dollars) of manufacturing one item will increase by $2 for a $1 increase in x if y is held constant.

Explanation / Answer

Solution:

a)

Substituting value of X = 18 , Y= 8 in C(X,Y) =40 +2X+8Y we get

C = 40+2*18+8*8 = 140 dollar

Thus cost of manufacturing one of these items is $140 dollars

b) Derivative of C(X,Y) = 2

It means that if Y is held constant cost increases by 2 dollar for every one dollar increase in X.

Hence last option is correct.

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