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
Andreas93 [3]
2 years ago
12

Find two positive integers such that the sum of the first number and four times the second number is 1000, and the product of th

e two numbers is as large as possible.
Mathematics
1 answer:
vladimir2022 [97]2 years ago
6 0

Answer:

The two numbers are:

x = 500

y = 125

Step-by-step explanation:

We want to find two numbers x and y, such that:

x + 4*y = 1000

f(x, y) = x*y is maximum.

From the first equation, we can isolate one of the variables to get

x = 1000 - 4y

now we can replace it in f(x, y):

x*y = (1000 - 4*y)*y  = 1000*y - 4*y^2

So now we want to maximize the function:

f(y) =- 4*y^2 + 1000*y

where y must be an integer.

Notice that this is a quadratic equation with a negative leading coefficient (so the arms of the graph will open downwards), thus, the maximum will be at the vertex.

Remember that for a general quadratic equation:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/(2*a)

so, in the case of:

f(y) =- 4*y^2 + 1000*y

the y-value of the vertex will be:

y = -1000/(2*-4) = 1000/8 = 125

So we found the value of y.

now we can use the equation:

x = 1000 - 4*y

x = 1000 - 4*125 = 1000 - 500 = 500

x = 500

Then the two numbers are:

x =500

y = 125

You might be interested in
Write an equation of a line in slope intercept form given the line passes through the points (-5, 3) and (0, -7)
insens350 [35]

Answer:

y=-2x-7

Step-by-step explanation:

Hope this helps, have a nice night! (^-^)

7 0
2 years ago
For 3x^2+5x-2 state the domain and range
FromTheMoon [43]
Domain is all real numbers. 

Range is all real numbers such that y is greater than -49/12
7 0
3 years ago
Help me with this questions please
mixas84 [53]
I) f(2)=1.5
ii) f(x)=0 ⇒ x=1.2
iii) k=-1
iv) x=1 ⇒ f(x)=1
4 0
2 years ago
Perpendicular lines intersect to form right angles.<br><br> always<br> sometimes<br> never
Ymorist [56]
Always- their slopes are always opposite reciprocals of each other
6 0
3 years ago
Read 2 more answers
What will it cost to carpet a rectangular floor measuring 21 feet by 12 feet if the carpet costs $29.56 per square yard?
Slav-nsk [51]

change the units to yards

21/3 = 7 yds

12/3 = 4 yds

A= 7*4 = 28 yds

cost = 29.56 * 28 = 827.68

the total cost is $827.68

6 0
3 years ago
Other questions:
  • Evaluate ( c + d ) 3 C=3 d=4
    15·1 answer
  • An angle is double its complement. find the angle and the complement
    15·2 answers
  • Emily was offered a job after college earning a salary of $35,000. She will get a raise
    11·1 answer
  • What is 1 minus 1 over 2
    10·2 answers
  • Draw and label the figure described MN and PQ intersecting at point R
    7·2 answers
  • Nicole drove six miles to Megan's house at thirty-seven mph. She then drove seventeen miles to Sarah's house. For the entire tri
    14·1 answer
  • What numbers are rational numbers
    5·1 answer
  • 15 is 23% of what number
    11·1 answer
  • Hi anyone here bored??​
    11·2 answers
  • I AM Confused on what to even do pls help
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!