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.
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.
Problem 53 Cut the largest possible rectangle from a circular quadrant, as shown in Fig. 40.
Problem 50 Find the shortest distance from the point (4, 2) to the ellipse x2 + 3y2 = 12.
Problem 48 Find the shortest distance from the point (5, 0) to the curve 2y2 = x3.
Problem 46 Given point on the conjugate axis of an equilateral hyperbola, find the shortest distance to the curve.
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?
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?
Problem 38 A cylindrical glass jar has a plastic top. If the plastic is half as expensive as glass, per unit area, find the most economical proportion of the jar.
Problem 35 A page is to contain 24 sq. in. of print. The margins at top and bottom are 1.5 in., at the sides 1 in. Find the most economical dimensions of the page.
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