1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Verdich [7]
3 years ago
15

A car rental agency has 150 cars. The owner finds that at a price of $48 per day, he can rent all the cars. For each $2 increase

in price, the demand is less and 4 fewer cars are rented. For each car that is rented, there are routine maintenance costs of $5 per day. What rental charge will maximize profit?
Mathematics
1 answer:
hram777 [196]3 years ago
3 0
Given that for each <span>$2 increase in price, the demand is less and 4 fewer cars are rented.

Let x be the number of $2 increases in price, then the revenue from renting cars is given by
(48 + 2x) \times (150 - 4x)=7,200+108x-8x^2.

Also, given that f</span><span>or each car that is rented, there are routine maintenance costs of $5 per day, then the total cost of renting cars is given by
5(150-4x)=750-20x

Profit is given by revenue - cost.
Thus, the profit from renting cars is given by
</span><span>(7,200+108x-8x^2)-(750-20x)=6,450+128x-8x^2

For maximum profit, the differentiation of the profit function equals zero.
i.e.
</span><span>\frac{d}{dx} (6,450+128x-8x^2)=0 \\  \\ 128-16x=0 \\  \\ x= \frac{128}{16} =8

The price of renting a car is given by 48 + 2x = 48 + 2(8) = 48 + 16 = 64.

Therefore, the </span><span>rental charge will maximize profit is $64.</span>
You might be interested in
Find a symbolic representation for f ^-1​(x).
Alexus [3.1K]

y = (9x) ^ (1/3)

exchange x and y  then solve for y

x = (9y) ^ (1/3)

cube each side

x^3 = 9y

divide each side by 9

1/9 x^3 = y

the inverse function is 1/9 x^3

4 0
3 years ago
Which is higher? 16 tons or 32,000 pounds?
yuradex [85]


their both equal or the 16 tons


6 0
3 years ago
Read 2 more answers
Which statements about the box plot are correct? Check all that apply. Fifty percent of the data values lies between 34 and 46.
Art [367]

Answer:

Option 1 and 3 are correct which indicate that fifty percent of the data values lie between 34 and 46, and it is unlikely there are any outliers.

Step-by-step explanation:

As the plot is not given, by an online search, same question is found online for which the plot is given as attached herewith.

From the box plot:

median=46

Q1=42

Q3=70

Q3-Q1= IQR=70-42=28

max=76

min=34

Range=max-min=76-34=42

no outliers seen from boxplot

only (1)and (3)are correct.

3 0
3 years ago
Read 2 more answers
NEED ANSWERS ASAP PLZZZ​
Sergio039 [100]
19 is 1:3 2:8 4:6 5:7
18 is I think... 2:4 1:7 3:5 8:6


7 0
3 years ago
Read 2 more answers
In the given polygon, AC= 5x - 24, AO= 3. Find x. NO LINKS!!!​
egoroff_w [7]

Answer:

x=6

Step-by-step explanation:

5x - 24 = 3 * 2

5x - 24 = 6

5x = 30

x = 6

5 0
2 years ago
Read 2 more answers
Other questions:
  • please help :) Respecting and understanding different opinions promotes fill in the blank . answer choices : (value/tolerance)
    5·1 answer
  • On a map, 1 inch equals 20 miles. two cities are 135 miles apart.what is the distance between the two cities on the map?
    5·1 answer
  • Jacob is working two summer jobs, making $10 per hour washing cars and making $8 per hour landscaping. In a given week, he can w
    15·1 answer
  • 8 is 40% of what number!<br> EXPLAIN please!! <br> Thank you!!
    11·1 answer
  • What is 98 2/3 as a decimal
    11·1 answer
  • Solve the following system using the addition method:
    14·2 answers
  • Factorize this equation . ײ-ײy²+×y ​
    11·1 answer
  • A pyramid has a square base whose side measures 23 dm. if the height is 14.5 dm, what is its volume?
    15·1 answer
  • AABC ~ AQRS
    12·1 answer
  • 40 POINTS!!!
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!