Question: A company plans to construct a new building and parking lot on a rectangular plot of land 100 meters wide and 120 meters long. The

A company plans to construct a new building and parking lot on a rectangular plot of land 100 meters wide and 120 meters long. The building is to be 20 meters high and to have a rectangular footprint with perimeter 320 meters, as shown in the accompanying figure.

100 m Building 120 m Parking lot

a. Express the volume V(x) of the building as a function of the length of its longer side x.

b. Graph the volume function in part (a), and determine the dimensions of the building of greatest volume that satisfies the stated requirements.

c. Suppose the company decides to construct the building of maximum volume. If it costs $75 per cubic meter to construct the building and $50 per square meter for the parking lot, what is the total cost of construction?

100 m Building 120 m Parking lot

Step by Step Solution

★★★★★

3.33 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Volume lengthwidthheight The height is given as 20 m and the perimeter is 3... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Calculus With Applications Questions!

Harmandeep Ltd. is a private company in the pharmaceutical industry. It has been preparing its financial statements in accordance with ASPE. Since it has plans to go public in the next 3 to 5 years,...

Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

What do you understand by overdraft protection?

Hello, This is the Fina 210 Course about Real estate. Could you help me to solve this problem and show me a solution? because i want to know how to solve this type of question in exam. Thank you! ps:...

because the firm dealt with many small businesses, some of which "went bankrupt" because they did not have the capital or strength to carry through from the production stage to market.) Often a small...

It was 3 a.m. when the wake-up call startled Steve McKenzie out of deep sleep. McKenzie, a management consultant from New Jersey, was glad to be finally leaving the Bon Star Hotel, a three-star hotel...

Mangaria For Ciniyay t Form a Mara MMM rd by Maan Maa Nay Ics trx year as Mash 2005, a 1 Maltate a nie , you start care with le + RC - salna - - at the a e parime they were they had hack change de...

Questions: Why is Wal-Mart successful in the US? What are its competitive advantages? Should Wal-Mart replicate its domestic model in its original form in China? Why? Can it build the same...

Hyatt's Problem Just what I don't need groaned Valerie Ferguson as she hung up the phone late one cold afternoon in December of 1993. Bad enough the weather stinks, and it gets dark by 4:30P, now...

19 Name: ____________________________________ 1. Your friend has a credit card with an APR of 49.9% ! What would his finance charge be on a $500 charge for just 1 month? 2. Your friend has 2 credit...

Find the value of df /dx at x = f(a). f(x) = x3 - 3x? - 4, x2 2, a = 5 45 1. 46 45

Viking Company purchased and installed carpet in its new general offices on June 30 for a total cost of $15,000. The carpet is estimated to have a 12-year useful life and no residual value. a....

Stefan is 2 7 years old and has a total AGI of $ 1 1 0 , 0 0 0 in 2 0 2 4 . He contracts an illness in 2 0 2 4 and incurs an unreimbursed medical bill that totals $ 7 , 5 0 0 . He withdraws $ 7 , 5 0...

1.1 Identify common misconceptions about the field of psychology. (APA 2.1) 1.2 Identify the four goals of psychological research. (APA 1.1, 2.1)

Suppose a cost-benefit model is given by where (x) is the cost (in thousands of dollars) of removing x percent of a certain pollutant from an area stream. (a) Find the rate of change of the cost with...

In Exercises, use the properties of limits to help decide whether each limit exists. If a limit exists, find its value. lim 00-X x + 2x - 5 3x + 2

The profit (in thousands of dollars) from the expenditure of x thousand dollars on advertising is given by P(x) = 1000 + 32x - 2x 2 . Find the marginal profit at the following expenditures. In each...

On September 1, Year 1, Able Company purchased a building from Regal Corporation by paying $420,000 cash and issuing a one-year note payable for the balance of the purchase price. Interest on the...

Wiater Company operates a small manufacturing facility. On January 1 , 2 0 2 1 , an asset account for the company showed the following balances: Equipment Accumulated Depreciation ( beginning of the...

MoonShine Company signed a note for $85,000 to purchase a new piece of equipment. MoonShine will pay the $85,000 back at the end of two years along with any accrued interest. The annual interest rate...