Calculus

Find two numbers such that the sum of the first plus three times the second is 600 and their product is a maximum.


x + 3y=600
xy is a max. This is the problem statement.

let U be the function equal to xy.

U=xy = y(600-3y)
Now, maximize U (take derivative, set to zero), and solve for y.


I see BobP. set this up, but let me clarify a little.
Let x and y be the two number, as Bob had, then x+3y=600 and P=x*y. Since this is only one variable calculus, we need to express y in terms of x, so from
x+3y=600 we have y=(600-x)/3 = 200-(1/3)x
Now use that function of x for y in the product to get
P=x*[200-(1/3)x]=200x - (1/3)x^2
Find dP/dx, set to 0 and solve. You should also be in the habit of testing the endpoints and any other critical values too, sometimes these questions can throw a curve at you.

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra

    One number is 4 times and then positive number. The sum of the two numbers is 620. Find the two numbers.

  2. math

    A number cube with sides labeled 1 through 6 is rolled two times, and the sum of the numbers that end face up is calculated. What is the probability that the sum of the numbers is 3?

  3. Algebra

    One number is 3 times another. If the sum of their reciprocals is 4, find the two numbers. __ 15 this is supposed to be 4 over 15 Let the smaller number be x. The two numbers are then x and 3x. You have only one unknown now. 1/x +

  4. Math

    Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the

  1. Math

    tHE SUM OF THREE NUMBERS IS 75. THE SECOND NUMBER IS 5MORE THAN THE FIRST AND THE THIRD IS THREE TIMES THE SECOND. FIND THE NUMBERS.

  2. Algebra I

    The sum of two numbers is 15. Three times one of the numbers is 11 less than five times the other. Find the numbers. Please help. ^.^

  3. Algebra

    the sum of 4 times one number and 3 times a second number is 64. If the sum of the two numbers in 19, find the two new numbers

  4. algebra

    the sum of two numbers is the same as four times the smaller number.if twice the larger is decreased by the smaller,the result is 30.find the numbers

  1. Algebra

    The sum of two numbers is 9. Four times the larger number plus three times the smaller number is 48. Find the numbers. Thank you

  2. high school (math)

    Match the mathematical expression with its translation. 1. the product of two numbers 2. y divided by x 3. six less than a number is y 4. x subtracted from y 5. the sum of two numbers is six 6. x minus y 7. the sum of x and y 8. x

  3. Math

    The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)

  4. Math

    four times one number minus a second is 11, and the sum of the numbers is 14. Find the numbers.

You can view more similar questions or ask a new question.