Chapter 14.3, Problem 5E

(a)

To determine

To calculate: The increase in total cost for each increase of $1 per pound of the raw material. The total cost of producing 1 unit of a product is given by $C\left(x,y\right)=20x+70y+\frac{x^2}{1000}+\frac{x{y}^2}{100}$ dollars, where x represents the cost per pound of raw materials and y represents the hourly rate for labor. The present cost for raw materials is $10 per round and the present hourly rate for labor is $24. Interpret the answer.

(b)

To determine

To calculate: The increase in total cost for each increase of $1 per hour in labor costs. The total cost of producing 1 unit of a product is given by $C\left(x,y\right)=20x+70y+\frac{x^2}{1000}+\frac{x{y}^2}{100}$ dollars, where x represents the cost per pound of raw materials and y represents the hourly rate for labor. The present cost for raw materials is $10 per round and the present hourly rate for labor is $24. Interpret the answer.