Maxima and Minima

58 - 59 Maxima and minima: cylinder surmounted by hemisphere and cylinder surmounted by cone

Problem 58
For the silo of Problem 57, find the most economical proportions, if the floor is twice as expensive as the walls, per unit area, and the roof is three times as expensive as the walls, per unit area.

56 - 57 Maxima and minima problems of square box and silo

Problem 56
The base of a covered box is a square. The bottom and back are made of pine, the remainder of oak. If oak is m times as expensive as pine, find the most economical proportion.

53 - 55 Solved Problems in Maxima and Minima

Problem 53
Cut the largest possible rectangle from a circular quadrant, as shown in Fig. 40.

50 - 52 Nearest distance from a given point to a given curve

Problem 50
Find the shortest distance from the point (4, 2) to the ellipse x2 + 3y2 = 12.

46 - 47 Solved Problems in Maxima and Minima

Problem 46
Given point on the conjugate axis of an equilateral hyperbola, find the shortest distance to the curve.

43 - 45 Solved problems in maxima and minima

Problem 43
A ship lies 6 miles from shore, and opposite a point 10 miles farther along the shore another ship lies 18 miles offshore. A boat from the first ship is to land a passenger and then proceed to the other ship. What is the least distance the boat can travel?

41 - 42 Maxima and Minima Problems Involving Trapezoidal Gutter

Problem 41
In Problem 39, if the strip is L in. wide, and the width across the top is T in. (T < L), what base width gives the maximum capacity?