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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 3.5, Problem 20E

Textbook Problem

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**Maximum Profit** A real estate office handles a 50-unit apartment complex. When the rent is $580 per month, all units are occupied. For each $40 increase in rent, however, an average of one unit becomes vacant. Each occupied unit requires an average of $45 per month for service and repairs. What rent should be charged to obtain a maximum profit?

To determine

**To calculate:** The rent need to be charge so as to obtain the maximum profit when the rent is

**Given Information:**

All the units are occupied when the rent is

**Formula used:**

The power rule for differentiation states that,

The derivative of a constant times a function is

The derivative of a sum/difference of terms in a function,

**Calculation:**

The number of apartment handle by the real estate is 50 unit.

Let

The primary equation for the profit is given as,

Where

Now, the value of

Therefore,

And the total cost can be calculated as

Therefore,

Using the above values in the primary equation

**Graph:**

The graph of the above function can be drawn using ti-83 calculator by following steps:

Step1: Press

Calculus: An Applied Approach (MindTap Course List)

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Maximum Profit The cost per unit of producing...Ch. 3.5 - Maximum Profit A real estate office handles a...Ch. 3.5 - Maximum Revenue When a wholesaler sold a product...Ch. 3.5 - Maximum Revenue A small theater has a seating...Ch. 3.5 - Minimum Cost A power station is on one side of a...Ch. 3.5 - Minimum Cost An offshore oil well is 1 mile off...Ch. 3.5 - Minimum Cost In Exercises 25 and 26, find the...Ch. 3.5 - Minimum Cost In Exercises 25 and 26, find the...Ch. 3.5 - Elasticity In Exercises 27-32, find the price...Ch. 3.5 - Elasticity In Exercises 27-32, find the price...Ch. 3.5 - Elasticity In Exercises 27-32, find the price...Ch. 3.5 - Elasticity In Exercises 27-32, find the price...Ch. 3.5 - Elasticity In Exercises 27-32, find the price...Ch. 3.5 - Elasticity In Exercises 27-32, find the price...Ch. 3.5 - Elasticity The demand function for a product is...Ch. 3.5 - Elasticity The demand function for a product is...Ch. 3.5 - Minimum Cost The shipping and handling cost C (in...Ch. 3.5 - Minimum Cost The ordering and transportation cost...Ch. 3.5 - Revenue The demand for a car wash is x=90045p,...Ch. 3.5 - HOW DO YOU SEE IT? Match each graph with the...Ch. 3.5 - Sales The sales S (in billions of dollars) for...Ch. 3.5 - Sales The sales S (in billions of dollars) for...Ch. 3.5 - Demand A demand function is modeled by x=apm where...Ch. 3.6 - Checkpoint 1 Worked-out solution available at...Ch. 3.6 - Checkpoint 2 Worked-out solution available at...Ch. 3.6 - Checkpoint 3 Worked-out solution available at...Ch. 3.6 - Checkpoint 4 Worked-out solution available at...Ch. 3.6 - Checkpoint 5 Worked-out solution available at...Ch. 3.6 - Checkpoint 6 Worked-out solution available at...Ch. 3.6 - Checkpoint 7 Worked-out solution available at...Ch. 3.6 - Checkpoint 8 Worked-out solution available at...Ch. 3.6 - In Exercises 1-8, find the limit. limx2(x+1)Ch. 3.6 - In Exercises 1-8, find the limit. limx1(3x+4)Ch. 3.6 - In Exercises 1-8, find the limit. limx32x2+x15x+3Ch. 3.6 - In Exercises 1-8, find the limit. limx34x29x9x3Ch. 3.6 - In Exercises 1-8, find the limit....Ch. 3.6 - In Exercises 1-8, find the limit. limx1x26x+5x21Ch. 3.6 - In Exercises 1-8, find the limit. limx0+xCh. 3.6 - In Exercises 1-8, find the limit. limx1(x+x1)Ch. 3.6 - In Exercises 9-12, find the average cost function...Ch. 3.6 - In Exercises 9-12, find the average cost function...Ch. 3.6 - In Exercises 9-12, find the average cost function...Ch. 3.6 - In Exercises 9-12, find the average cost function...Ch. 3.6 - Vertical and Horizontal Asymptotes In Exercises...Ch. 3.6 - Vertical and Horizontal Asymptotes In Exercises...Ch. 3.6 - Vertical and Horizontal Asymptotes In Exercises...Ch. 3.6 - Vertical and Horizontal Asymptotes In Exercises...Ch. 3.6 - Vertical and Horizontal Asymptotes In Exercises...Ch. 3.6 - Vertical and Horizontal Asymptotes In Exercises...Ch. 3.6 - Finding Infinite Limits In Exercises 7-12, find...Ch. 3.6 - Finding Infinite Limits In Exercises 7-12, find...Ch. 3.6 - Finding Infinite Limits In Exercises 7-12, find...Ch. 3.6 - Finding Infinite Limits In Exercises 7-12, find...Ch. 3.6 - Finding Infinite Limits In Exercises 7-12, find...Ch. 3.6 - 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The graph shows the temperature...Ch. 3.6 - Seizing Drugs The cost C (in millions of dollars)...Ch. 3.6 - Recycling Bins The cost C (in dollars) of...Ch. 3.6 - Learning Curve Psychologists have developed...Ch. 3.7 - Checkpoint 1 Worked-out solution available at...Ch. 3.7 - Checkpoint 2 Worked-out solution available at...Ch. 3.7 - Checkpoint 3 Worked out solution available at...Ch. 3.7 - Checkpoint 4 Worked-out solution available at...Ch. 3.7 - Checkpoint 5 Worked-out solution available at...Ch. 3.7 - In Exercises 1-4, find the vertical and horizontal...Ch. 3.7 - In Exercises 1-4, find the vertical and horizontal...Ch. 3.7 - In Exercises 1-4, find the vertical and horizontal...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 122, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 122, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 122, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 122, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Interpreting a Graph In Exercises 37-40, use the...Ch. 3.7 - Interpreting a Graph In Exercises 37-40, use the...Ch. 3.7 - Interpreting a Graph In Exercises 37-40, use the...Ch. 3.7 - Interpreting a Graph In Exercises 37-40, use the...Ch. 3.7 - Sketching a Function In Exercises 41 and 42,...Ch. 3.7 - Sketching a Function In Exercises 41 and 42,...Ch. 3.7 - Creating a Function In Exercises 43 and 44, create...Ch. 3.7 - Creating a Function In Exercises 43 and 44, create...Ch. 3.7 - 45. 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Revenue The revenue R for a company selling x...Ch. 3.8 - Demand The demand function for a product is...Ch. 3.8 - HOW DO YOU SEE IT? The graph shows the profit P...Ch. 3.8 - Biology: Wildlife Management A state game...Ch. 3.8 - Medical Science The concentration C (in milligrams...Ch. 3.8 - Marginal Analysis A retailer has determined that...Ch. 3.8 - Marginal Analysis The demand x for a web camera is...Ch. 3.8 - Error Propagation In Exercises 41 and 42, use the...Ch. 3.8 - Error Propagation In Exercises 41 and 42, use the...Ch. 3.8 - True or False? In Exercises 43 and 44, determine...Ch. 3.8 - True or False? 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Maximum Profit A commodity has a demand...Ch. 3 - Maximum Profit The profit P (in thousands of...Ch. 3 - Elasticity The demand function for a product is...Ch. 3 - Elasticity The demand function for a product is...Ch. 3 - Finding Vertical Asymptotes In Exercises 67-70,...Ch. 3 - Finding Vertical Asymptotes In Exercises 67-70,...Ch. 3 - Finding Vertical Asymptotes In Exercises 67-70,...Ch. 3 - Finding Vertical Asymptotes In Exercises 67-70,...Ch. 3 - Determining Infinite Limits In Exercises 71-74,...Ch. 3 - Determining Infinite Limits In Exercises 71-74,...Ch. 3 - Determining Infinite Limits In Exercises 71-74,...Ch. 3 - Determining Infinite Limits In Exercises 71-74,...Ch. 3 - Finding Horizontal Asymptotes In Exercises 75-78,...Ch. 3 - Finding Horizontal Asymptotes In Exercises 75-78,...Ch. 3 - Finding Horizontal Asymptotes In Exercises 75-78,...Ch. 3 - Finding Horizontal Asymptotes In Exercises 75-78,...Ch. 3 - 79. Average Cost The cost C (in dollars) of...Ch. 3 - 80. Average Cost The cost C (in dollars) of...Ch. 3 - Seizing Drugs The cost C (in millions of dollars)...Ch. 3 - Removing Pollutants The cost C (in dollars) of...Ch. 3 - Analyzing a Graph In Exercises 8394, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Bacteria The data in the table show the number N...Ch. 3 - Meteorology The monthly average high temperature T...Ch. 3 - Comparing y and dy In Exercises 97-100, compare...Ch. 3 - Comparing y and dy In Exercises 97-100, compare...Ch. 3 - Comparing y and dy In Exercises 97-100, compare...Ch. 3 - Comparing y and dy In Exercises 97-100, compare...Ch. 3 - Marginal Analysis In Exercises 101-106, use...Ch. 3 - Marginal Analysis In Exercises 101-106, use...Ch. 3 - Marginal Analysis In Exercises 101-106, use...Ch. 3 - Marginal Analysis In Exercises 101-106, use...Ch. 3 - Marginal Analysis In Exercises 101-106, use...Ch. 3 - Marginal Analysis In Exercises 101-106, use...Ch. 3 - Finding Differentials In Exercises 107-112, find...Ch. 3 - Finding Differentials In Exercises 107-112, find...Ch. 3 - Finding Differentials In Exercises 107-112, find...Ch. 3 - Finding Differentials In Exercises 107-112, find...Ch. 3 - Finding Differentials In Exercises 107-112, find...Ch. 3 - Finding Differentials In Exercises 107-112, find...Ch. 3 - Profit The profit P (in dollars) for a company...Ch. 3 - Demand The demand function for a product is...Ch. 3 - Physiology: Body Surface Area The body surface...Ch. 3 - In Exercises 1-3, find the critical numbers and...Ch. 3 - In Exercises 1-3, find the critical numbers and...Ch. 3 - In Exercises 1-3, find the critical numbers and...Ch. 3 - In Exercises 4-6, use the First-Derivative Test to...Ch. 3 - In Exercises 4-6, use the First-Derivative Test to...Ch. 3 - In Exercises 4-6, use the First-Derivative Test to...Ch. 3 - In Exercises 7-9, find the absolute extrema of the...Ch. 3 - In Exercises 7-9, find the absolute extrema of the...Ch. 3 - In Exercises 7-9, find the absolute extrema of the...Ch. 3 - In Exercises 10-13, discuss the concavity of the...Ch. 3 - In Exercises 10-13, discuss the concavity of the...Ch. 3 - In Exercises 10-13, discuss the concavity of the...Ch. 3 - In Exercises 10-13, discuss the concavity of the...Ch. 3 - In Exercises 14 and 15, find all relative extrema...Ch. 3 - In Exercises 14 and 15, find all relative extrema...Ch. 3 - In Exercises 16-18, find the vertical and...Ch. 3 - In Exercises 16-18, find the vertical and...Ch. 3 - In Exercises 16-18, find the vertical and...Ch. 3 - In Exercises 19-21, analyze and sketch the graph...Ch. 3 - In Exercises 19-21, analyze and sketch the graph...Ch. 3 - In Exercises 19-21, analyze and sketch the graph...Ch. 3 - 22. Find the value of dy when and . Compare this...Ch. 3 - A commodity has a demand function modeled by...

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When choosing k elements from a set of n elements, order may or may not matter and repetition may or may not be...

Discrete Mathematics With Applications

Find the sum: 40 + 37 + 34 + 31 + 28 + 25 + 22.

College Algebra