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
kumpel [21]
3 years ago
10

A company manufactures and sells x television sets per month. The monthly cost and​ price-demand equations are ​C(x)=74,000+80x

and p(x)=300− x 30​, 0≤x≤9000. ​(A) Find the maximum revenue. ​(B) Find the maximum​ profit, the production level that will realize the maximum​ profit, and the price the company should charge for each television set. ​(C) If the government decides to tax the company ​$5 for each set it​ produces, how many sets should the company manufacture each month to maximize its​ profit? What is the maximum​ profit? What should the company charge for each​ set?
Mathematics
1 answer:
SOVA2 [1]3 years ago
3 0

Answer:

a) $675000

b) $289000 profit,3300 set, $190 per set

c) 3225 set, $272687.5 profit, $192.5 per set

Step-by-step explanation:

a) Revenue R(x) = xp(x) = x(300 - x/30) = 300x - x²/30

The maximum revenue is at R'(x) =0

R'(x) = 300 - 2x/30 = 300 - x/15

But we need to compute R'(x) = 0:

300 - x/15 = 0

x/15 = 300

x = 4500

Also the second derivative of R(x) is given as:

R"(x) = -1/15 < 0 This means that the maximum revenue is at x = 4500. Hence:

R(4500) = 300 (4500) - (4500)²/30 = $675000  

B) Profit P(x) = R(x) - C(x) = 300x - x²/30 - (74000 + 80x) = -x²/30 + 300x - 80x - 74000

P(x) = -x²/30 + 220x - 74000

The maximum revenue is at P'(x) =0

P'(x) = - 2x/30 + 220= -x/15 + 220

But we need to compute P'(x) = 0:

-x/15 + 220 = 0

x/15 = 220

x = 3300

Also the second derivative of P(x) is given as:

P"(x) = -1/15 < 0 This means that the maximum profit is at x = 3300. Hence:

P(3300) =  -(3300)²/30 + 220(3300) - 74000 = $289000  

The price for each set is:

p(3300) = 300 -3300/30 = $190 per set

c) The new cost is:

C(x) = 74000 + 80x + 5x = 74000 + 85x

Profit P(x) = R(x) - C(x) = 300x - x²/30 - (74000 + 85x) = -x²/30 + 300x - 85x - 74000

P(x) = -x²/30 + 215x - 74000

The maximum revenue is at P'(x) =0

P'(x) = - 2x/30 + 215= -x/15 + 215

But we need to compute P'(x) = 0:

-x/15 + 215 = 0

x/15 = 215

x = 3225

Also the second derivative of P(x) is given as:

P"(x) = -1/15 < 0 This means that the maximum profit is at x = 3225. Hence:

P(3225) =  -(3225)²/30 + 215(3225) - 74000 = $272687.5

The money to be charge for each set is:

p(x) = 300 - 3225/30 = $192.5 per set

When taxed $5, the maximum profit is $272687.5

You might be interested in
Best answer gets brainiest. On Wednesday at camp, Diana went for a hike at 5:35 A.M. The hike took 1 hour and 30 minutes. As soo
Ratling [72]

Answer:

8:00am I'm not sure, sorry if I get it wrong dude...

7 0
3 years ago
The sum of three times the larger of two integers and twice the smaller is seven the difference between the two integers is four
Aloiza [94]

Answer:

x=3   y=-1

Step-by-step explanation:

3x+2y=7

x-y=4

4 0
3 years ago
A. Rotation of 180º and then a reflection across the x-axis.
Trava [24]

C.

Hope this helps!

Please vote brainliest

3 0
3 years ago
Write an equation in slope-intercept form for the line with slope 1/4 and y intercept -4. Then graph the line​
quester [9]

Answer:

Step-by-step explanation:

slope intercept form is y = mx + b

b is the y intercept ( crossing y axis value)....     by inspection   b = -4

m is the slope of the line,  Slope = m = 1/4      note: the slope is positive

the slope equals the 'rise' over 'run'  

if the line moves up the slope is positive, if the line moves down the slope is negative

the rise is how many y units does the line go 'up' or 'down'

the run is how many x units does the line go 'left' or 'right'

the rise = 1  Y unit

the run = 4 X units

y = mx + b    m =1/4  b = -4

y = (1/4)x + (-4)

y = (1/4)x - 4

graph a line stating at y = -4 and going up (rising) to the right ONE Y Unit for  every FOUR X units (the run)

3 0
3 years ago
Marcus is traveling from Rome to Capua on the Via Appia (a 132 mile journey). His horse and cart travels at 8 mph. How long will
nalin [4]

Answer: 16.5 hours

Step-by-step explanation:

distance=rate*time

132=8*x

Divide by 8 on both sides

x=16.5

6 0
3 years ago
Other questions:
  • Find the GCF of 5 and 7.
    10·2 answers
  • Determine dy/dx in terms of t and evaluate it at the given value of t for the following parametric curves.a. x = 3 sin t, y = 2
    10·1 answer
  • Jovian decided to collect data to determine if students' heights and their shoe sizes are correlated. He determined the data to
    5·1 answer
  • Because of knee problems, Kelly has been warned not to jog more than 15 miles a week. If she jogs three times a week, what is th
    15·2 answers
  • Mrs. Rodriquez has 24 students in her class. Ten of the students are boys. Jeff claims that the ratio of boys to girls in this c
    12·1 answer
  • Multiply. Express your answer in lowest terms. 3/8 x 2/7 = ?/?
    14·2 answers
  • A patient weighs 93 pounds (lb). Meperidine hydrochloride is ordered for pain at a dosage of 6 milligrams (mg) per kilogram of b
    7·1 answer
  • Solve for x in the diagram below. 15 points :3
    11·1 answer
  • ILL MARK AS BRAINLESS HELP PLS
    7·2 answers
  • 2. Which is an
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!