Exam 8: Functions of Several Variables

Which of the following describes the contour diagram of ?

The following table shows the revenue R, (in hundreds of dollars) at a movie theater as a function of the number of tickets sold, t, and the number of snacks sold, f. Thus, . Assuming there is only one price for tickets, what is that price?

The profit, P, from producing a product is expressed as a function of the cost, C, of producing the product and the revenue, R, from selling the product. Do you expect P to be an increasing or decreasing function of R?

For , calculate h s

The following table shows the revenue R, (in hundreds of dollars) at a movie theater as a function of the number of tickets sold, t, and the number of food items sold, f. Thus, . What is the revenue when ticket sales are 300 and food sales are 600?

The amount of principal, $P, needed to obtain a balance of $B after t years at r % interest, compounded continuously, is given by the formula . Which of the following gives the amount principal can be changed by and still maintain the same balance if there is an increase of 1% in the interest rate?

Below is a contour diagram depicting D, the average fox population density as a function of , kilometers east of the western end of England, and , kilometers north of the same point. Is D increasing or decreasing at the point (120, 25) in the northern direction?

The production function for a company is , where P is the amount produced given x units of labor and y units of equipment. Each unit of labor costs $900 and each unit of equipment costs $350. Assuming the goal of the company is to minimize cost given a fixed production goal of 6000 units produced, what are the objective and constraint functions?

Is (0, 0) a critical point of the following function?

A television salesman earns a fixed salary of $9.00 per hour plus a $25 commission for each television he sells. If h is the number of hours worked and s is the number of televisions sold, find a formula for , the salesman's total earnings. Is E an increasing or decreasing function of s?

A company operates two plants that make the same product. If Plant 1 produces quantity x of the product and Plant 2 produces quantity y of the product, the cost functions are and . The total market demand for the product is related to the selling price p by . What quantity should Plant 1 produce to maximize the company's profit?

Suppose . Then has a local minimum value of 9 at the point (2, 3) when A = _____, B = _____, and C = _____.

Which of the following contour diagrams is more likely to show the population density of a region of a small town where the center of the diagram is the town center? I. II.

The quantity, Q, of a good produced depends on the number of workers, W, and the amount of capital invested, K, according to the Cobb-Douglas function . If the maximum production level at a budget of $2500 is 973 and , estimate the production if the budget is increased by $100.