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
Vesna [10]
3 years ago
6

A concession stand at an athletic event is trying to determine how much to sell cola and iced tea for in order to maximize reven

ue. Let x be the price per cola and y the price per iced tea. Demand for cola is 100 – 34x + 5y colas per game and iced tea is 50 + 3x – 16y iced teas per game The concession stand should charge: dollars per cola, dollars per iced tea, in order to maximize revenue. The maximum revenue for one game is: dollars.
Mathematics
1 answer:
Cerrena [4.2K]3 years ago
4 0

Solution :

Demand for cola : 100 – 34x + 5y

Demand for cola : 50 + 3x – 16y

Therefore, total revenue :

x(100 – 34x + 5y) + y(50 + 3x – 16y)

R(x,y)  = $100x-34x^2+5xy+50y+3xy-16y^2$

$R(x,y) = 100x-34x^2+8xy+50y-16y^2$

In order to maximize the revenue, set

$R_x=0, \ \ \ R_y=0$

$R_x=\frac{dR }{dx} = 100-68x+8y$

$R_x=0$

$68x-8y=100$  .............(i)

$R_y=\frac{dR }{dx} = 50-32x+8y$

$R_y=0$

$8x-32y=-50$  .............(ii)

Solving (i) and (ii),

4 x (i)    ⇒       272x - 32y = 400

     (ii)   ⇒   (-<u>)     8x - 32y = -50   </u>

                        264x        = 450

∴   $x=\frac{450}{264}=\frac{75}{44}$

     $y=\frac{175}{88}$

So, x ≈  $ 1.70      and    y = $ 1.99

    R(1.70, 1.99) = $ 134.94

Thus, 1.70 dollars per cola

          1.99 dollars per iced ted to maximize the revenue.

Maximum revenue = $ 134.94

You might be interested in
5. For which equation is the ordered pair (-3,4) a solation?
liraira [26]
Don’t click the file above it’s you may get a virus because you could simply just say the answers instead of here’s a file . And the answer is A
8 0
3 years ago
Read 2 more answers
What would 85% of 690 lbs be?
Elodia [21]
 85% of 690 lbs would be 586.5

5 0
3 years ago
Read 2 more answers
A group of hikers walked 8 and 7/10 miles. And then 5 and 1/5 miles. How far did they walk altogether?
Anton [14]
13 and 9/10 miles altogether
5 0
3 years ago
The decimal 0.4444 is an example of what kind of number
Slav-nsk [51]
That would be a decimal!
5 0
2 years ago
If tan θ = 3/2 and cos θ &lt; 0, use the fundamental identities to evaluate the other five trig functions of θ.
notsponge [240]
Use the Pythagorean theorem, tan is y/x so y = -3 and x= -2. Because cos is negative and R is always positive. You need to find R- which is the hypotenuse;
3^2 + 2^2 = r^2
9 + 4 = r^2
13 = r^2
√13 = r.

So you already have tan<span>θ, 
cot</span><span>θ= 2/3

sin</span>θ= -3/√13 BUT
you have to rationalize, so you get -3 √13/ 13

cscθ= √13/ -3

cosθ= -2/ √13 BUT
you have to rationalize, so you get -2√13/ 13

secθ= √13/ -2
4 0
3 years ago
Read 2 more answers
Other questions:
  • From least to greates -4 3/7, -4 5/6, -5 3/7, 4 2/7, 5 1/7
    10·1 answer
  • If two planes intersect, they intersect in exactly one ?
    6·2 answers
  • Does anyone know how to do this?
    15·1 answer
  • Which statement about the angle measures is true?
    7·2 answers
  • Helppppp pleaseee :)
    5·1 answer
  • 7. If a school has 70 computers in the ratio of 3 desktops for every 4 laptops, how many
    6·1 answer
  • Trey is solving his equation, and the last line of his work is "-2 = 2". What does this mean?
    7·1 answer
  • For the parallelogram find the value of x,y,and z
    15·1 answer
  • Is 23 a prime number
    10·1 answer
  • ...............................................................So help.
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!