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Calculus
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13 Nov 2019

DIRECTION:

Show all work – facts, primary and secondary equations, finding the derivatives, doing sign tests, and don’t forget to answer the questions asked!

1. An ecologist is conducting a research project on breeding pheasants in captivity. She must first construct suitable pens. She wants a rectangular region with two additional fences as shown in the diagram. Find the maximum area that can be enclosed with 3000 meters of fencing.

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Keith Leannon
Keith LeannonLv2
21 May 2019

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Related questions

A total of 2000 square feet is to be enclosed in two pens, as illustrated. The outside walls are to be constructed of brick, and the inner dividing wall is to be constructed of chain link. The brick wall costs $10 per linear foot and the chain link costs $5 per linear foot. Find the dimensions x and y that minimize the cost of construction.

Chain link


Brick

show all work – facts, primary and secondary equations, finding the derivatives, doing sign tests, and don’t forget to answer the questions asked!

DIRECTION:

Show all work – facts, primary and secondary equations, finding the derivatives, doing sign tests, and don’t forget to answer the questions asked!

1. An appliance firm is marketing a new refrigerator. It determines that in order to sell x refrigerators, the price per refrigerator must be p = 280 – 0.4x. It also determines that the total cost of producing x refrigerators is given by C (x) = 5000 + 0.6x2 . How many refrigerators must the company produce and sell in order to maximize profit? What is the maximum profit?

DIRECTION:

Show all work – facts, primary and secondary equations, finding the derivatives, doing sign tests, and don’t forget to answer the questions asked!

1. A canvas wind shelter for the beach is to be constructed of 96 square feet of canvas that has been donated by a local company. The wind shelter is to have a back, two square sides and a top (see figure). What should be the dimensions of the shelter so that the space inside the shelter will be maximized?

2. A building supply store wants to build a rectangular outdoor storage facility on the rear wall of its building. An iron fence will enclose the facility on 3 sides and the wall of the building will be the fourth side. Find the dimensions of the storage facility with the largest area that can be built with 200 feet of fencing.

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