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
timama [110]
3 years ago
12

You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). O

ne week you charged $9 per guest and averaged 165 guests per night. The next week you charged $10 per guest and averaged 150 guests per night.
(a) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p. q(p) =
(b) Find the nightly revenue R as a function of the cover charge p. R(p) =
(c) The club will provide two free non-alcoholic drinks for each guest, costing the club $2 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $1,000. Find the cost C as a function of the cover charge p. C(p) =
(d) Now find the profit in terms of the cover charge p. P(p) =
Determine the entrance fee you should charge for a maximum profit. p = $ per guest.
Mathematics
1 answer:
Neko [114]3 years ago
5 0

Answer:

a)q(p)=-15p+ +300

b)R(p)=-15p²+300p

c)C(p)=-30p+1600

d.1)P(p)=-15p²+330p-1600

d.2)p=$11

Step-by-step explanation:

(a).Before getting started, we are going to consider  the cartesian plane, where x-axis corresponds to the cover charge and y-axis corresponds to number of guests per night . There, we will locate the following coordinates according to the previous information:

(9,165)  (10,150).

Remember that  the slope-intercept form of the  linear equation is y=mx+b where m is the slope and b  is te intercept.

The slope can be calculated  by the next formula:

m=\frac{y2-y1}{x2-x1}

In this case we will assign  (9,165) as the first coordinate and (10,150) as the second one. The order does not matter. At the end we get the same value for m.

Therefore:

m=\frac{150-165}{10-9} = -15

Now, we have the slope and two poitns. According to this, and taking into account that  point-slope form of the equation of a line is y-y1=m(x-x1),   find a linear demand equation.

Any of two coordintates can be selected. In this case we will select the second one.

y-150=-15(x-10)   equation 1

Solve equation 1 for y

y=-15x+150+150

y=-15x+300

Above we had defined x as cover charge (p) and y as number of guests (q). Thus, rewrite equation 1.

q(p)=-15p+ +300.  

it equation shows the number of guests per night as a function of the cover charge,

(b). The nightly revenue can be calculated multplying the price of the cover charge by  the number of guests. So, we just have to multiply the equation 1 by p.

p*q(p)=p*(-15p +300)

R(p)=-15p²+300p   equation 2

(c) To get the cost function of the nightclub  we just have to multiply the cost of the two non-alcoholic drinks   by the number of the guests ( equation 1) and add to it  nightly overheads.

C(p)=2*(-15p+300)+1000

C(p)= -30p+600+1000

C(p)=-30p+1600  equation 3

(d) In order to find the profit in terms of the cover charge we will  subtract nightly costs ( equation 3) from nightly revenue (equation 2)

P(p)=R(p)-C(p)

P(p)=-15p²+300p - (-30p+1600)

P(p)=-15p²+300p+30p-1600

P(p)=-15p²+330p-1600

To determine that  the entrance fee we should charge for a maximum profit we are going to use the first derivative test (y'(x)=0) in order to find an extremum point.

Compute the first derivative of P(p)

P'(p)=-30p+330=0

30p=330

p=330/30

p= $11

The entrance fee that we should charge for a maximum profit is p=$11 per guest.

You might be interested in
Pleaseeee help please​
kumpel [21]

Answer: It will be 60m^2

5 0
2 years ago
What is the surface area of a box with a height and width of 5 inches and a length of 8 inches ?
vodomira [7]

Answer:

210 sq in

Step-by-step explanation:

Box dimensions: 5 x 5 x 8

2 faces: 5 x 5 -> 2 * 5 * 5 = 50

4 faces: 5 x 8 -> 4 * 5 * 8 = 160

Total = 50 + 160 = 210 sq in

5 0
3 years ago
True or False: The following sequence of numbers is an arithmetic sequence.
slava [35]

Answer:

False

Step-by-step explanation:

3 0
3 years ago
3-v=4 solve for v help me please
Novay_Z [31]

3 - v = 4

- v = 4-3

-v = 1

v = -1

5 0
3 years ago
Read 2 more answers
There are 24 students in a class. 2 have three or more siblings. Half have two siblings. One-third have one sibling, and the res
tigry1 [53]

two children are only children

5 0
3 years ago
Read 2 more answers
Other questions:
  • How does a digit in the ten thousands place compare to one in the thousands place
    9·1 answer
  • Is that right? <br><br> If not please help me out.
    8·1 answer
  • I need help with this whole math page
    13·1 answer
  • What is the place value of the 6 in 0.896?
    6·2 answers
  • $9500 is invested, part of it at 11% and part of it at 8%. For a certain year, the total yield is $937.00. How much was invested
    6·1 answer
  • The base charge of a cab in new york is $2.50 as soon as you enter the cab. There is an additional charge of $2.50 per mile trav
    9·2 answers
  • What is the quotient of 28 divided by 7 increased by 4
    13·2 answers
  • What is the 3rd root of 125
    15·1 answer
  • UP TO 50 POINTS ON BRAINLY
    14·1 answer
  • We have a shape that has an area of 112 inches squared. Convert the units to centimeters squared. (HINT: Perform multiple conver
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!