A prize winning animal is going to be shown at the State Fair. A pen must be constructed to hold the animal. The rectangular pen will have three wooden sides, which cost 30 dollars per foot to construct. The front of the pen will be made of a special reinforced glass, which costs 45 dollars per foot to construct. The animal requires an area of 60 square feet in order to be comfortable. Figure 1. Schematic drawing of animal enclosure If the pen is to be built as cheaply as possible, what are the dimensions of the pen that should be built? Length of glass front of pen : __feet Depth of pen : __feet How much will the pen cost to build? Cost of pen : __dollars Give all your answers correct to two decimal places.
A prize winning animal is going to be shown at the State Fair. A pen must be constructed to hold the animal.
The rectangular pen will have three wooden sides, which cost 30 dollars per foot to construct. The front of the pen will be made of a special reinforced glass, which costs 45 dollars per foot to construct.
The animal requires an area of 60 square feet in order to be comfortable.
Figure 1. Schematic drawing of animal enclosure
- If the pen is to be built as cheaply as possible, what are the dimensions of the pen that should be built?
Length of glass front of pen : __feet
Depth of pen : __feet
- How much will the pen cost to build?
Cost of pen : __dollars
Give all your answers correct to two decimal places.
Given information:
Three sides of the pen are made by wood and the one side made by glass.
Construct the wooden side with the cost 30 dollars per foot.
Construct the glass side with the cost 45 dollars per foot.
Animal requires 60 square feet area to enter the pen comfortably.
To find:
a) The dimensions of the pen in order to minimize the cost of construction.
b) Minimum cost of construction.
Concept used:
i) Area of the rectangle is the product of the length and width.
ii) Second derivative test:
If , then function attains minimum at .
If , then function attains maximum at .
Here, is the critical point of the function.
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none of the answers above were correct...is there a different way this problem could be solved? still very confused on it
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