5. Find two positive numbers whose sum is 110 and whose product is a maximum.

Q: Find two numbers whose sum is a , if the product of one by the cube of the other is to be a maximum.

A: We have to find number

Q: Find three positive numbers whose sum is 300 and whose product is a maximum.

A: Let x ,y,z are 3 positive numbers such that x+y+z = 300 and xyz is maximumThe problem formed…

Q: 6. Find two numbers whose sum is a, if the product of the square of the one by the cube of the other…

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Q: product

A: We will solve the problem.

Q: Find three positive numbers whose sum is 310 and whose product is a maximum.

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Q: 12. Show that a rectangle with given perimeter has maximum area when it is a square.

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Q: Find the maximum product of two positive numbers given that the sum of the first number and twice…

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Q: 12. Of all numbers whose sum is 70, find the two that have the maximum product.

A: let x and y be two numbers whose sum is 70   we have to maximize  M=xy where x+y=70

Q: Find two positive numbers whose sum is 14 and the sum of whose squares is minimum

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Q: Find three positive numbers whose sum is 100 and whose product is a maximum.

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Q: Suppose that x and y are two positive numbers, and suppose that r+ 2y = 30. Find the maximum value…

A: Given that: x+2y=30…

Q: Suppose you have a 2.5 grade point average in 3 courses. What is the minimum average you can have in…

A:

Q: Find two non-negative numbers whose sum is 59  and whose product is a minimum.

A:

Q: 2. Find two numbers whose sum is 50 and whose product is a maximum.

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Q: Find the maximum area of a rectangle in the first quadrant where one side of the rectangle lies…

A:

Q: Find two numbers whose sum is a if the product of the square of one by the cube of the other is to…

A: Consider the first number be 'x'. The second number be 'y'. The sum of the numbers is given by a.…

Q: 1. The sum of two numbers is 12. What are these numbers if the product of the first and the cube of…

A: Given problem Given that   The sum of two numbers = 12 Let the two numbers be x and y. We have to…

Q: Q1. The sum of three positive numbers is 30, find the three numbers if their product is minimum?

A: Topic- Number System

Q: 13. Of all numbers whose difference is 6, find the two that have the minimum product.

A: Let x and y be such numbers. x-y=6 P=xy. Substitute x=6+y in P=xy and obtain that P=y6+y=6y+y2.

Q: Find three positive numbers whose sum is 90 and whose product is a maximum.

A: Second derivative test: For critical points, fx=0 fy=0 A function f(x,y) has a local maximum value…

Q: What is the difference between the maximum and minimum of the quantity (x2y2)/25 where x and y are…

A:

Q: Goes through (0, -2) and has a local maximum at (1, 3) f(x) = 5x² - 10x - 2 O B) f(x) = -5x² + 10x +…

A:

Q: 1. Find two numbers whose sum is 9 if the product of one by the square of the other is a maximum.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 11. What is the minimum product of two numbers whose difference is 18?

A: lets' numbers are x,x-18 where; x>x-18 so, productp of them will be p=xx-18=x2-18x now, product…

Q: What are two positive numbers with a product of 250 where the sum of the first and four times the…

A: Let the positive numbers are x and y.Given that the product of them is = 250So, xy=250or, y=250x

Q: 23. Find two numbers whose sum is 10 and the sum of their squares is a minimum.

A: Let the two numbers be  x and yx+y=10⇒y=10-xx2+y2=SS=x2+10-x2   =x2+x2-20x+100   =2x2-20x+100

Q: Find two numbers with difference 130 and whose product is a minimum.

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Q: Find two positive numbers whose product is 50 such that the sum of the first plus 2 times the second…

A: Given, Product of 2 positive number is 50  First number+2(second number)=S, is a minimum.

Q: 1. The sum of two positive number is 42. What are these numbers if their product is a maximum?

A: As per our guidelines we can help you in solving only first question. Rest of the problems, you have…

Q: 3. Find two positive read numbers such that the sum of the first number squared and the second…

A: Let the numbers are x and y. x2 + y = 48 .................(1) y = 48 - x2   The product of two…

Q: What is the largest possible product you can form from two non-negative numbers whose sum is 56? The…

A: To find: largest possible product you can form from two non-negative numbers whose sum is 56

Q: 6. Find two positive numbers such that the sum of twice the first number and three times the second…

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Q: Find two numbers whose sum is a, if the product of one by the cube of the other is to be a maximum.

A: According to our guidelines In case of multiple questions we are supposed to answer the first…

Q: 1. The product of two numbers is 147. If the sum of one of the numbers and thrice the other is to be…

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Q: at the one-dimensional and n are constants.

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Q: Find two numbers whose sum is 20 and whose product is maximum?

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Q: Multivariable optimization question

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Q: Find three positive numbers x, y, and z whose sum is 21 and product is a maximum.

A: There are two different questions in the image. According to our guidelines, we can solve only one…

Q: What is the difference between the maximum and minimum of the quantity x2y2/87, where x and y are…

A:

Q: 4. The sum of two positive numbers is 30. One of the numbers is multiplied by the square of the…

A:

Q: Suppose that x and y are two positive numbers, and suppose that x + 2y = 30. Find the maximum value…

A: Given data:   The first equation is x+2y=30. The expression for the function is f(x,y)=(x+1)(y+3).…

Q: Find three positive numbers whose sum is 400 and whose product is a maximum.

A: Let 3 numbers be x, y, z Sum of these numbers is 400 x+y+z = 400          z= 400-x-y Product = P(x,…

Q: 4. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: For minimum , second derivative of the function should  be positive.

Q: A home gardener estimates that 19 apple trees will have an average yield of 147 apples per tree. But…

A: Total  number of apple  trees=x+19GIVEN:Additional tree planted the yield will decrease by three…

Q: Find a pair of non-negative numbers that have a product of 162 and minimize the sum of two times the…

A: Let the numbers be x,y. Given  x·y=162y=162x The function to be minimized will be Fx=2x+y…

Q: Find two numbers whose sum is 11 and product is a maximum?

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Q: 11. Determine three positive numbers whose sum is 21, so that your product is the maximum possible…

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Q: Suppose x and y are positive integers such that the sum of x^2 and y is 10x. Find the values of x…

A: Given x^2+y=10x.From there find y.

Q: Find two positive numbers whose product is 2 and the sum of one number and the square of the other…

A: Let x and y be the required numbers. Given that the product of two numbers is 2. That is, Now…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.