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
Lunna [17]
3 years ago
14

The John Deere company has found that revenue, in dollars, from sales of heavy-duty tractors is a function of the unit price p,

in dollars, that it charges. If the revenue R is R(p)=-1/2 p^2+1900p, please answer the following questions:
Part A: How much revenue will the company generate if they sell 700 tractors?

Part B: How many tractors does the company want to sell to maximize the revenue?

Show your work/explain your answers please!

Mathematics
1 answer:
lys-0071 [83]3 years ago
8 0

<u>Answer-</u>

<em>A- 700 tractors will generate a revenue of $1,085,000</em>

<em>B- The company must sell 1900 tractors in order to maximize the revenue.</em>

<u>Solution-</u>

The John Deere company has found that the revenue from sales of heavy-duty tractors is a function of the unit price p, in dollars, that it charges. If the revenue R, in dollars, is

R(p)=-\frac{1}{2}p^2+1900p

<u>How much revenue will the company generate if they sell 700 tractors:</u>

\Rightarrow R(p)=-\frac{1}{2}(700)^2+1900(700)

\Rightarrow R(p)=1,085,000

Therefore, 700 tractors will generate a revenue of $1,085,000

<u>How many tractors does the company want to sell to maximize the revenue</u>

By calculating the value of p for which R(p) is maximum will be the number of tractors for which the revenue will be maximum. We can take the help of derivatives to find this.

R(p)=-\frac{1}{2}p^2+1900p

Taking the derivative w.r.t p,

\Rightarrow R' (p)=-\frac{1}{2}\times 2\times p+1900

\Rightarrow R' (p)=-p+1900

\Rightarrow R' (p)=1900-p

Taking R'(p) = 0, to find out the critical points

\Rightarrow R' (p)=0

\Rightarrow 1900-p=0

\Rightarrow p=1900

So, at p = 1900, the function R(p) will be maximum. The maximum value will be,

\Rightarrow R(p)=-\frac{1}{2}(1900)^2+1900(1900)

\Rightarrow R(p)=1,805,000

Therefore, the company must sell 1900 tractors in order to maximize the revenue and the maximum revenue will be $1,805,000.


You might be interested in
In the diagram below, we have ST parallel to QR. angle P= 40 degrees, and angle Q= 35 degrees. Find the measure of angles STR in
Drupady [299]

Answer:

m\angle S = 35^\circ, \ m\angle T = 105^\circ,\ m\angle R = 105^\circ

Step-by-step explanation:

<u>Similar Triangles</u>

Lines ST and QR are parallel. Thus, angles S and Q are congruent, and angles T and R are congruent.

Considering the triangle PQR, the sum of its internal angles must be 180°:

m\angle P + m\angle Q + m\angle R = 180^\circ

Substituting the known values:

40^\circ + 35^\circ + m\angle R = 180^\circ

Solving for R:

m\angle R = 180^\circ - 40^\circ - 35^\circ

m\angle R = 105^\circ

Angles S and Q are congruent, thus

m\angle S = 35^\circ

Angles T and R are congruent, thus

m\angle T = 105^\circ

Summarizing:

\mathbf{m\angle S = 35^\circ, \ m\angle T = 105^\circ,\ m\angle R = 105^\circ}

7 0
3 years ago
Read 2 more answers
What is the least common multiple of 32 24 and 18
noname [10]

Answer:

288 is your answer. Your welcome

3 0
3 years ago
Read 2 more answers
The equation is (9+6)+4=(5+ blank)+4​
rusak2 [61]
10 is your answer!! hope this helps
4 0
3 years ago
Read 2 more answers
The price of a bracelet increased from $170 to $200 on Mother's Day.
ivanzaharov [21]
So 200 - 170  = 30 , 30 is 17.6470588235% so the answer would be B)18%
7 0
3 years ago
Read 2 more answers
Which is greater 5 pounds or 85 ounces
kolbaska11 [484]
85 ounces because there are 16oz in 1lb. 85/16 is 5.31
4 0
3 years ago
Read 2 more answers
Other questions:
  • 79 divided by 50,165
    13·1 answer
  • Jordan Michael runs a basketball camp. A group of randomly selected camp participants were asked to give their shirt size. The t
    11·2 answers
  • Express 55 in standard form​
    8·1 answer
  • What is the x-intercepts of the function f(x)=-2x2-3x+20
    12·2 answers
  • How can you tell if an ordered pair is a solution of a system of linear equations by examining the graphs of the equations?
    13·1 answer
  • Student spend 5 minutes of every 60 minutes at school moving from class to class. Which fraction is equivalent to the number of
    12·1 answer
  • What is the area of this figure?
    12·1 answer
  • Pls I need help for this questionnn
    15·1 answer
  • Correct answer gets brainliest
    5·1 answer
  • What is one thousand minus on hundred and ten
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!