Example of business applications, Mathematics

Assignment Help:

An apartment complex contains 250 apartments to rent.  If they rent x apartments then their monthly profit is specified by, in dollars,,                                      P ( x ) = -8x2 + 3200x - 80, 000

How several apartments must they rent in order to maximize their profit?

Solution : All that we're actually being asked to do is to maximize the profit subject to the constraint that x must be in the range 0 ≤ x ≤ 250 .

Firstly, we'll required the derivative & the critical point(s) which fall in the range 0 ≤ x ≤ 250

P′  (x)  =-16x + 3200 ⇒        3200 -16 x = 0                 ⇒   x = 3200/ 16 = 200

As the profit function is continuous and we have an interval with finite bounds we can determine the maximum value through simply plugging in the only critical point which we have (that nicely enough in the range of acceptable answers) and the ending points of the range.

P (0) = -80, 000    P ( 200) =240, 000       P ( 250) = 220, 000

therefoer, it looks like they will produce the most profit if only they rent out 200 of the apartments rather than all 250 of them.

There are couples of very real applications to calculus which are in the business world and at some level i.e. the point of this section.  Note as well that to actually learn these applications and all of their intricacies you'll have to take a business course or two or three.  In this section we're only going to scratch the surface & get a feel for some of the real applications of calculus from the business world and some main "buzz" words in the applications.


Related Discussions:- Example of business applications

Need help , understandin rates and unitrates

understandin rates and unitrates

Total accumulation of the amount deposited in saving account, A bank pays o...

A bank pays on its savings an interest rate of 6% per year but compounds interest monthly (i.e., estimates the interest each month and adds it to the balance).  You plan to deposit

What is larry''s salary after the raise, Larry earned $32,000 per year. The...

Larry earned $32,000 per year. Then he received a (3)1/4% rise. What is Larry's salary after the raise? If Larry earns a (3) 1/4 % (or 3.25%) raise, he will earn 103.25% of his

Solving geometry using algebra, if one side of a square is increased 4 inch...

if one side of a square is increased 4 inches and an adjacement side is multiplied by 4, the perimeter of the resulting rectangle is 3 times the perimeter of the square. find the s

Relative measures of dispersion, Relative measures of dispersion Defi...

Relative measures of dispersion Definition of Relative measures of dispersion: A relative measure of dispersion is a statistical value that may be utilized to compare va

How to solving one-step equations, How to Solving One-Step Equations? E...

How to Solving One-Step Equations? Equations, where one math operation is acting on the variable, can be solved in one step. The trick is to get the variable x by itself - isol

Kurtosis-measure of central tendency, Kurtosis - It is a concept, whic...

Kurtosis - It is a concept, which refers to the degree of peakedness of a described frequency distribution. The degree is generally measured along with reference to general di

GEOMETRIC PROGRESSION, THE FIRST AND THIRD TERM OF A G.P ARE 8 AND 18 RESPE...

THE FIRST AND THIRD TERM OF A G.P ARE 8 AND 18 RESPECTIVELY AND THE COMMON RATIO IS POSITIVE.FIND THE COMMON RATIO

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd