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
Andru [333]
3 years ago
9

A local artist working at the town fair makes caricatures and portraits. The caricatures cost $4 to make white

Mathematics
1 answer:
il63 [147K]3 years ago
8 0

Answer:

The artist should make 15 caricatures and 30 portraits.

Step-by-step explanation:

First, we identify the variables for the problem. In this case, the variables will be:

C=number of caricatures

P= number of portraits.

Next, we can use the variables to make the inequalities that constrain the problem.

We know the artist can't spend more than $360 for supplies and we also know that it costs $4 to make a caricature and $10 to make a portrait, so:

4C+10P\le 360

We also know the artist has a limit of time of 20 hours, which is the same as 20*60=1200 minutes to paint. We know it takes her 20 minutes to make a caricature and 30 minutes to make a portrait, so:

20C+30P\le 1200

and we also know she must make a positive number of caricatures and a positive number of portraits so the other two constrains are:

C\ge 0

P\ge 0

So we can go ahead and graph them. (see attached picture)

Once we graphed the inequalities we can determine what the corners of the polygon created by the intersection of the shaded areas are, so we proceed and calculate them:

first point:

(0,0)

second point:

4(0)+10P=360

P=\frac{360}{10}

P=36

(0,36)

Third point:

20C+30(0)=1200

C=\frac{1200}{20}

C=60

(60,0)

Fourth point:

4C+10P = 360

20C+30P = 1200

We multiply the first equation by -5 so we get:

-20C-50P=-1800

20C+30P=1200

------------------------

-20P=-600

P=30

so:

20C+30(30)=1200

20C=1200-900

20C=300

C=15

(15,30)

Once we found the 4 points, we go ahead and evaluate them for the objective function. In this case, the objective function is the total amount of money she got from selling the pieces of art, so we get:

I=10C+20P

Point 1

I=10(0)+20(0)=0

Point 2

I=10(0)+20(36)=720

Point 3

I=10(60)+20(0)=600

Point 4

I=10(15)+20(30)=750

Next, we look for the greatest income which in this case will be 750 so that's why she must make 15 caricatures and 30 Portraits.

You might be interested in
The lifetime of two light bulbs are modeled as independent and exponential random variables X and Y, with parameters lambda and
Scorpion4ik [409]

Answer:

\bf h(x)=max(\lambda,\mu) e^{-max(\lambda,\mu) x}\;(x\geq0)

Step-by-step explanation:

The PDF of X is

\bf f(x)=\lambda e^{-\lambda x}\;(x\geq0)

The PDF of Y is

\bf g(x)=\mu e^{-\mu x}\;(x\geq0)

The means of X and Y are respectively,

\bf \displaystyle\frac{1}{\lambda}\;,\displaystyle\frac{1}{\mu}

so we can see that the larger the parameter, the smaller the mean. Hence the PDF of Z = min(X, Y) is an exponential with the largest parameter of the two.

Therefore, the PDF of Z is

\bf h(x)=max(\lambda,\mu) e^{-max(\lambda,\mu) x}\;(x\geq0)

7 0
3 years ago
In biology class, Kaylee observes cells. Each cell has a structure that separates the inside of the cell from the environment. W
ella [17]
The plasma membrane
Both prokaryotic and eukaryotic cells have a plasma membrane, a double layer of lipids that separates the cell interior from the outside environment.
8 0
3 years ago
Read 2 more answers
Question 6
marin [14]

Answer:

18 miles per hour is an outlier

the outlier decreases the mean speed

Step-by-step explanation:

the low number of 18 is way different from the other numbers being in the 30's and 40's

this 18 will bring the mean of all the numbers own because it is a smaller number.

8 0
3 years ago
I need help on this one question. Please help me. Find the area of the shaded region. It says round to the nearest tenth if nece
schepotkina [342]
30.44 but it depends how you do the problem
5 0
3 years ago
The graph of y = cosine (x + pi/2) is the graph of the y = cos(x) shifted in which direction?
kap26 [50]

Answer:

pi/2 units to the left

Step-by-step explanation:

Kono Dio Da!!!!

5 0
3 years ago
Read 2 more answers
Other questions:
  • The answer to 2z+10=3z+20
    7·2 answers
  • Write an equation of the line in point slope form: A line that passes through (4,-5) with a slope of -6 (Show Work)
    15·1 answer
  • I don't get this at all and it's confusing me
    10·1 answer
  • An octagon is a polygon with eight sides. Which of the following
    9·1 answer
  • A bicycle store costs $2800 per month to operate. The store pays an average of $80 per bike. The average selling price of each b
    13·1 answer
  • Column A Column B
    11·1 answer
  • A spy is trying to escape. She must get by four guards. Each guard takes half of her remaining money. She then $64 for her plane
    6·1 answer
  • What is the domain of this quadratic function?
    15·2 answers
  • केविन अपनी छुट्टी के लिए स्नोबोर्डिंग जाना चाहता था। बताएं कि वह बॉक्स प्लॉट्स से बर्फबारी के आंकड़ों के आधार पर रिज़ॉर्ट ए या र
    13·1 answer
  • Line passes through the point (8,4) and a slope of 5/4. Write equation in slope-intercept
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!