Word Problems on Differentiation

profileHomework Tutor
 (Not rated)
 (Not rated)
Chat

1) A farmer decides to make 3 identical pens with 144 feet of fence. The pens will be next to each other sharing a fence and will be up against a barn. The barn side needs no fence. What dimensions for the total enclosure (rectangle including all pens) will make the area as large as possible?

 

2) Water is falling on a surface, wetting a circular area that is expanding at a rate of dA/dt = 3 mm^2/s. How fast is the radius of the wetted area expanding, dr/dt, when the radius is 181 mm? (round approximations to four decimal places.)

 

3) A hotel has 220 units. All rooms are occupied when the hotel charges $70 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant. Each occupied room costs $24 per day to service and maintain. What should the hotel charge per day in order to maximize daily profit?

 

4) A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is twice as long as it is wide. Find the dimensions of the box produced from the minimum amount of material.

 

5) Of all numbers whose sum is 450, find the two that have the maximum product.

    • 9 years ago
    Solutions to Word Problems on Differentiation
    NOT RATED

    Purchase the answer to view it

    blurred-text
    • attachment
      solutions_to_word_problems_on_differentiation.doc