The quantity of a product demanded by consumers is a function of its price. The quantity

Figure 8.47 shows contours of f(x, y). List the x- and y-coordinates and the value of the function at any local maximum and local minimum points, and identify which is which. Are any of these local extrema also global extrema on the region shown? If so, which ones? 1 2 3 4 5 6 7 8 9 2 4 6 8 10 12 14 16 x y 8 9 7 2 1 3 4 5 6 6 5 7 8 9 Figure 8.47

Figure 8.48 shows contours of f(x, y). List x- and ycoordinates and the value of the function at any local maximum and local minimum points, and identify which is which. Are any of these local extrema also global extrema on the region shown? If so, which ones?

In Problems 35, estimate the position and approximate value of the global maxima and minima on the region shown.

In Problems 35, estimate the position and approximate value of the global maxima and minima on the region shown.

In Problems 35, estimate the position and approximate value of the global maxima and minima on the region shown.

In Problems 615, find all the critical points and determine whether each is a local maximum, local minimum, a saddle point, or none of these. f(x, y) = x2 + 4x + y2

In Problems 615, find all the critical points and determine whether each is a local maximum, local minimum, a saddle point, or none of these. f(x, y) = x2 + xy + 3y

In Problems 615, find all the critical points and determine whether each is a local maximum, local minimum, a saddle point, or none of these. f(x, y) = x2 + y2 + 6x 10y + 8

In Problems 615, find all the critical points and determine whether each is a local maximum, local minimum, a saddle point, or none of these. f(x, y) = y3 3xy +6x

In Problems 615, find all the critical points and determine whether each is a local maximum, local minimum, a saddle point, or none of these. f(x, y) = x3 + y2 3x2 + 10y + 6

In Problems 615, find all the critical points and determine whether each is a local maximum, local minimum, a saddle point, or none of these. f(x, y) = x3 + y3 6y2 3x +9

In Problems 615, find all the critical points and determine whether each is a local maximum, local minimum, a saddle point, or none of these. f(x, y) = x3 + y3 3x2 3y +10

In Problems 615, find all the critical points and determine whether each is a local maximum, local minimum, a saddle point, or none of these. f(x, y) = x2 2xy + 3y2 8y

In Problems 615, find all the critical points and determine whether each is a local maximum, local minimum, a saddle point, or none of these. f(x, y) = x3 3x + y3 3y

In Problems 615, find all the critical points and determine whether each is a local maximum, local minimum, a saddle point, or none of these. f(x, y) = 400 3x2 4x + 2xy 5y2 + 48y

By looking at the weather map in Figure 8.5 on page 358, find the maximum and minimum daily high temperatures in the states ofMississippi, Alabama, Pennsylvania, New York, California, Arizona, and Massachusetts.

For f(x, y) = A (x2 + Bx + y2 + Cy), what values of A, B, and C give f a local maximum value of 15 at the point (2, 1)?

Amissile has a guidance devicewhich is sensitive to both temperature, tC, and humidity, h. The range in kmover which the missile can be controlled is given by Range = 27,800 5t2 6ht 3h2 + 400t + 300h. What are the optimal atmospheric conditions for controlling the missile?

The quantity of a product demanded by consumers is a function of its price. The quantity of one product demanded may also depend on the price of other products. For example, if the only chocolate shop in town (a monopoly) sells milk and dark chocolates, the price it sets for each affects the demand of the other. The quantities demanded, q1 and q2, of two products depend on their prices, p1 and p2, as follows: q1 = 150 2p1 p2 q2 = 200 p1 3p2. (a) What does the fact that the coefficients of p1 and p2 are negative tell you? Give an example of two products that might be related this way. (b) If one manufacturer sells both products, how should the prices be set to generate the maximum possible revenue? What is that maximum possible revenue?

Two products are manufactured in quantities q1 and q2 and sold at prices of p1 and p2, respectively. The cost of producing them is given by C = 2q2 1 + 2q2 2 + 10. (a) Find the maximum profit that can be made, assuming the prices are fixed. (b) Find the rate of change of that maximum profit as p1 increases.

A company operates two plants which manufacture the same item and whose total cost functions are C1 = 8.5 + 0.03q2 1 and C2 = 5.2 + 0.04q2 2 , where q1 and q2 are the quantities produced by each plant. The company is a monopoly. The total quantity demanded, q = q1 + q2, is related to the price, p, by p = 60 0.04q. How much should each plant produce in order to maximize the companys profit