1. Functions of Several Variables OBJECTIVE Find a function value for a function of several variables.

2. Example 1: For the profit function, find P(25, 10).

3. Example 2: The total cost to a company, in thousands of dollars, is given by where x dollars is spent for labor, y dollars for raw materials, z dollars for advertising, and w dollars for machinery. Find C(3, 2, 0, 10).

4. Example 3: A business purchases a piece of storage equipment that costs C 1 dollars and has capacity V 1. Later it wishes to replace the original with a new piece of equipment that costs C 2 dollars and has capacity V 2. Industrial economists have found that in such cases, the cost of the new piece of equipment can be estimated by the function of three variables

5. Example 3 (cont.): For $45,000, a beverage company buys a manufacturing tank that has a capacity of 10,000 gallons. Later it decides to buy a tank with double the capacity of the original. Estimate the cost of the new tank.