The product of two positive real numbers, x and y, is 14. Determine the y value which minimizes the value of x + 4y

Q: A company that produces cell phones has a cost function of C = 9x - 55x + 5652, where C is the cost…

A:

Q: A manufacturer of open steel boxes has to make one with a square base and a volume of 1 m3. The…

A: Given that ,Volume of open steel box = 1m3    volume of box = x.x.ysteel cost $2 per square unit(a)…

Q: The price of A is $16 per unit and the price of B is $2 per unit and you will spend $128. How many…

A: It is given that the price of A is $16 per unit and the price of B is $2 per unit. The amount to…

Q: A piece of wire 75m long and needs to be divided into two pieces. One piece will be used to form a…

A: Given data: The total length of the wire is L=75 m. The expression for the total length which is…

Q: A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then divide…

A: Given query is to find the way of fency to minimize the cost.

Q: A company that produces cell phones has a cost function of C = cost in dollars and x is the number…

A:

Q: A wire 7 meters long is cut into two pieces. One piece is bent into a equilateral triangle for a…

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Q: 1. The sum of two positive numbers is 200. What is the maximum possible value for their product? 2.…

A: As question number is not mentioned in the given attachment. So, I am solving first question. Kindly…

Q: A rectangular page is to contain 50 square inches of print. The page has to have a 1-inch margin on…

A: GivenArea of printed  pages=50in2Margin at top and bottom =1 inchMargin on each side=12 inch

Q: A company that produces cell phones has a cost function of C = 6x² – 197x + 1859, where C is the…

A: C= 6x2-197x+1859differentiating w.r.t xC'=12x-197+0C'=012x-197=0x=19712

Q: A company that produces cell phones has a cost function of C = 4x2 – 56x + 8972, where C is the cost…

A: Given query is to find the number of unit to minimize the cost.

Q: A patient's pulse measures 75bpm, 82bpm, then 108bpm. To determine an accurate measurement of pulse,…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: The product of two positive numbers is 588. The sum of the first and three times the second is…

A: Let the two numbers be x and y. Here, the product of two numbers is, xy=588.     ... (1) Sum of x…

Q: A wire 7 meters long is cut into two pieces. One piece is bent into a equilateral triangle for a…

A:

Q: The product of two positive real numbers, x and y , is 30 . Determine the y value which…

A: Given product of two positive real number x and y is 30. ⇒xy=30 Let fx,y=x+4y And gx,y=xy−30=0 Use…

Q: A piece of wire 20 m long is cut into two pieces. One piece is bent into a square and the other is…

A: The area and circumference of the circle is πr2, 2πr respectively, where r is the radius of the…

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

A: Topic- Number System

Q: A company that produces cell phones has a cost function of C = 15x² cost in dollars and æ is the…

A: Given: C(x)=15x2−365x+5783where,C→Cost in dollarsx→Number of cell phones produced (in thousands)

Q: A company that produces cell phones has a cost function of C = 20x² and x is the number of cell…

A: The given cost function is Cx=20x2-515x+1724. We need to find the number of units of cell phone that…

Q: A company that produces cell phones has a cost function of C = 4x² – 50x + 13298, where C is the…

A:

Q: A farmer wants to fence an area of 13.5 million square feet in a rectangular field and then divide…

A:

Q: Two chemical factories are discharging toxic waste into a large lake, and the pollution level at a…

A: The given function is,

Q: A small island is 5 miles from the nearest point P on the straight shoreline of a large lake. If a…

A: Let 'x' be the distance from point to the landing position. Given situation in graph is represent as

Q: 13. A rectangular dog pen of 800 sq. feet is to be constructed as shown. The cost is $5 per running…

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Q: A patient's pulse measures 72 beats per minute, 73 beats per minute, and then 97 beats per minute.…

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Q: why minimize ||A x – b|| + A ||x|| and minimize ||A x – b||² + A ||x||2 are the same?

A: Consider the terms of the given function one by one Now the given function of x gives always the…

Q: Find two positive integers such that their sum is 10, and minimize the sum of squares.

A: Given  two positive integers such that their sum is 10, To minimize the sum of squares

Q: Find the number in the interval[-5,5] so that the sum of six times the number and its square is…

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Q: An advertisement consists of a rectangular printed region plus 1-inch margins on the sides and…

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Q: A company that produces cell phones has a cost function of C = 3x² - 46x + 15097, where C' is the…

A:

Q: A company that produces cell phones has a cost function of C = 112² - 244x + 12581, where C is the…

A: The cost function is given as: C=11x2-244x+12851   We know that, at the minimum value, the…

Q: A company that produces cell phones has a cost function of C = 20x² - 541x + 22940, where C' is the…

A: This question can be solved using the concept of maxima and minima.

Q: A patient's pulse measures 70 bpm, 80 bpm, then 120 bpm. To determine an accurate measurement of…

A:

Q: A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it…

A: Given data are 24mil sq ft area of fence so pit area of rectangle and perimeter as given below

Q: Two positive numbers x and y add up to 100. What values of x and y will minimize 1² + 3y?

A: Given that x>0 ,y>0 and x+y=100 To find the values of x and y such that x2+3y will minimize.…

Q: A rectangular poster is to contain 128 square inches of print. The margins at the top and bottom of…

A: Let the length of the rectangle be x Length after 1 inches of margin = x-2  inch The breadth of…

Q: The fencing of the left border costs $5 per foot, while the fencing of the lower border costs $1 per…

A: Find  left border ft = bottom border ft = garden area ft2.

Q: The difference of two real numbers is d, where d is a fixed number. What two numbers will minimize…

A: Let the real numbers are x and y Given that y-x=d or y=x+d Product of them=P=xy=x(x+d)=x2+dx

Q: Minimize F = 24x2 + 24y2 with xy2 = 16.

A: Minimize F = 24x2 + 24y2 with xy2 = 16.

Q: A farmer wants to fence an area of 600 square feet in a rectangular field and then divide it in half…

A: Given that, A farmer wants to fence an area of 600 square feet in a rectangular field. After that,…

Q: Find the value of x that minimizes average cost if the cost function is C = x2 +5x+72

A:

Q: A company that produces cell phones has a cost function of C = 21æ² – 555x + 14960, where C is the…

A:

Q: A company that produces cell phones has a cost function of C = 25x² – 174x + 22200, where C is the…

A: Given cost function is,

Q: Find the point P on the line y = 5x that is closest to the point (52,0).  What is the least distance…

A: Given:The equation of the line is y = 5x.(52,0) is the closest point to the point P which line on…

Q: Find the point P on the line y = 5x that is closest to the point (52,0). What is the least distance…

A: Given that point P lies on the line y=5x. We need to find : i) the point P on the line y=5x that is…

Q: A company that produces cell phones has a cost function of C(x) = x² - 1200x + 36400, where C is the…

A: NOTE: Refresh your page if you can't see any equations.   . the cost function is  here we have a…

Q: A management company is going to build a new apartment complex. They know that if the complex…

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Q: A company that produces cell phones has a cost function of C = 12x2 – 89x + 16981, where C the cost…

A:

Q: You want to build a 1200 square foot rectangular infinity pool. Three of the sides will have regular…

A:

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: