110 Answered Questions for the topic Optimization

Optimization Math Calculus

18d

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 𝑇 = 200 (𝑒^x/10 + 𝑒^−𝑥/10). Find the maximum and minimum tension if the cable extends from 𝑥 = 10 to 𝑥 = −10... more
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 (it’s a straight road). The road runs parallel to the main highway that is 16km away.... more
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 (it’s a straight road). The road runs parallel to the main highway that is 16km away.... more
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 you’re 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... more
Optimization Calculus Derivatives

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... more
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... more
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... more
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... more
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 position AA, must reach someone who is drowning on the exact opposite side of the pool, at position CC. The... more
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... more
Optimization Math Geometry

10/30/20

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... more
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 radius r and length h as shown. The material needed for the two flat... more
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... more
Optimization Economics Microeconomics

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... more
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... more
Optimization Math Calculus Volume

07/04/20

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... more
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... more
Optimization Calculus Max/min

01/09/20

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 circular cylinder.  The tank must have a volume of 4000 cubic feet.  The material for the lateral surface costs $5... more
Optimization Math Calculus Related Rates

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... more
Optimization Math Calculus Related Rates

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... more
Optimization Java Logic Bit Manipulation

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... more

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