110 Answered Questions for the topic Optimization

#### A cable hangs in a curve that is symmetrical with respect to the y-axis.

The tension, T (in Newtons) of the cable at a point x metres from the y-axis is given by đ = 200 (đ^x/10 + đ^âđ„/10). Find the maximum and minimum tension if the cable extends from đ„ = 10 to đ„ = â10...
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Optimization Calculus

20d

#### Amount of wire needed

Another friend of the Lee family, the Bloch family, has a cottage that is situated 8km down the road from them (itâs a straight road). The road runs parallel to the main highway that is 16km away....
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Optimization Calculus

20d

#### how to minimize the total amount of wire needed

Another friend of the Lee family, the Bloch family, has a cottage that is situated 8km down the road from them (itâs a straight road). The road runs parallel to the main highway that is 16km away....
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Optimization Calculus

04/06/21

#### How do I find the point closest to (0,-7) for the hyperbola 7x^2-2y^2=20?

So I know that this is a classic optimization problem where youâre looking for the minimum value and use the distance formula. I think the arithmetic is what is hanging me up. The answer I got for...
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03/22/21

#### Application of Derivatives and Optimization of Volume

Using Calculus, determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 384 square centimeters. Can someone explain using derivative...
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Optimization Calculus

02/18/21

#### A particle P moves in a straight line so that at t seconds, its displacement, s meters from the starting point is s = t^3 - 7t^2 + 17t.

A particle P moves in a straight line so that at t seconds, its displacement, s meters from the starting point is s = t^3 - 7t^2 + 17t. Determine the interval of the time when the particle is...
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Optimization Calculus

02/06/21

#### A market is supplied n thousands of crates of watermelons daily when it is sold at d dollars per crate and the supply equation is dn - 3d - 100n - 100 = 0.

If the daily supply is decreasing by 250 crates per day, at what rate is the price changing when the daily supply is 5000 crates?

02/05/21

#### Calculus problem for my youngest son!

A store is given n thousands of crates of lemons daily when it is sold at c pesos per crate and the supply equation iscn - 3c - 100n - 100 = 0If the day by day supply is diminishing by 250 crates...
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Optimization Calculus

02/04/21

#### A market is supplied n thousands of crates of watermelons daily when it is sold at d dollars per crate and the supply equation is pn - 3p - 100n - 100 = 0.

If the daily supply is decreasing by 250 crates per day, at what rate is the price changing when the daily supply is 5000 crates?

Optimization Calculus

02/04/21

#### Optimization problem - maximum volume and maximum face area of a parallelepiped.

I've been working on this optimization question for a while now and just can't get it figured out. Here's the information that the question provides...A 6 m long metal rod is cut into 12 sections...
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Optimization Calculus

11/02/20

#### How would I solve for part 2?

Consider a lifeguard at a circular pool with diameter 43 meters. The lifeguard, at positionÂ AA, must reach someone who is drowning on the exact opposite side of the pool, at positionÂ CC. The...
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Optimization Calculus

11/02/20

#### Calculus Applied Optimization sec 4.7

Consider a wire of length 11ft. The wire is to be cut into two pieces of length x and 11-x. Suppose the length x is used to form a circle of radius r and the length 11-x is used to form a square...
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#### Complete the table to investigate the ticket price if the goal is to maximize the revenue

The promotion manager of a new band is deciding how much to charge for concert tickets. She has calculated that if tickets are $28 each, then 220 people will come to the concert. For every $1...
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Optimization Calculus

10/30/20

#### A gardener is building a shed to protect his plants from hot weather.

A gardener is building a shed to protect his plants from hot weather. Its shape is the surface of a half cylinder with radiusÂ rÂ and lengthÂ hÂ as shown. The material needed for the two flat...
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Optimization Calculus

10/15/20

#### Optimization Question

With the upcoming football season, we need to keep Mator the Gator safe fromthe coronavirus! Caden and Rebecca have decided to build him a pen in the shape ofan isosceles triangle with the vertex...
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10/10/20

#### Find the demands for goods X and Y for agent

Agent B's preferences are given by:U (x,y) = y - ((x)^(-2))/2Which are quasi-linear preferencesBudget constraint is -> x*p +y = 10(Since p= price of good x, and Price of good y is normalized to...
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Optimization Calculus

08/05/20

#### Optimization/ Extreme Value Problem

you are an engineer for Jiffy box Company. it is your job to design an open topped( that is, no top) cardboard box with a square base. The box must have a volume of 134 cubic inches of space...
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#### shipping volume

size = length + 2*width + 2*heightThe size of the package must be less than 165" and length has to be less than 108".You work for a producer who ships rectangular boxes that are 13"x4"x4". The...
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Optimization Calculus

05/04/20

#### How to solve This calc 1 problem

A realtor wishes to enclose 600 of land in a rectangular plot and then divide it into 2 rectangular pens with an interior fence parallel to two of the sides. What are the dimensions of...
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#### Find the area of the largest isosceles triangle that can be inscribed in a circle of radius r = 14 (see figure).

Solve for the area, and write as a function of h and then as a function of a.

Optimization Calculus

12/06/19

#### Optimization Calculus Question

An industrial tank is formed by adjoining two hemispheres to the ends of a right circularÂ cylinder.Â Â The tank must have a volume of 4000 cubic feet.Â Â The material for the lateralÂ surface costs $5...
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12/04/19

#### Optimization and Related Rates problem

This question uses the inverse-square law, which states that the light intensity experienced at a distance x from a light source is proportional to the luminosity of the source times x^(-2).It is...
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12/04/19

#### Optimization and Related Rates problem

This question uses the inverse-square law, which states that the light intensity experienced at a distance x from a light source is proportional to the luminosity of the source times x^(-2).It is...
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Optimization Statistics

07/29/19

#### a box is to be constructed with a total volume of 6400âcm^3. The sides cost $5 per cm^2, the top and bottom cost $4 per cm^2 . What are the dimensions that have the correct volume, but minimize cost?

06/19/19

#### Fastest way to get sign in Java?

I'd like to get the sign of a `float` value as an `int` value of -1 or 1.
Avoiding conditionals is always a good idea in reducing computational cost. For instance, one way I can think of would be...
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