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Practise Problems
Problem 1:
Find the dimensions of a rectangle with 1000 area. Let its parameter to be as small as possible.
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Model 2:
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Problem 2:
A child’s rectangular play yard is to be built next to the house. To make the three sides of the playpen, twenty-four feet of fencing are available. What should be the dimensions of the sides to make a maximum area?
Problem 3:
An open-top cylindrical tank with a volume of ten cubic feet is to be made from a sheet of steel. Find the dimensions of the tank that will require as little material used in the tank as possible.
Problem 4:
A cylindrical can is to hold 20 pm.3 The material for the top and bottom costs $10/m.2 and material for the side costs $8/m.2 Find the radius r and height h of the most economical can.
Problem 5:
You are standing at the edge of a slow-moving river which is one mile wide and wish to return to your campground on the opposite side of the river. You can swim at 2 mph and walk at 3 mph. You must first swim across the river to any point on the opposite bank. From there walk to the campground, which is one mile from the point directly across the river from where you start your swim. What route will take the least amount of time ?
Problem 6:
Car B is 30 miles directly east of Car A and begins moving west at 90 mph. At the same moment car A begins moving north at 60 mph. What will be the minimum distance between the cars and at what time t does the minimum distance occur ?
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