You are given a rectangular piece of cloth with dimensions X by Y, where X and Y are positive integers, and a list of n products that can be made using the cloth. For each product i in [1,n] you know that a rectangle of cloth of dimensions ai by bi is needed and that the final selling price of the product is ci. Assume that ai, bi, and ci are all positive integers. You have a machine that can cut any rectangular piece of cloth into two pieces either horizontally or vertically. Design an algorithm that finds the best strategy for cutting an X by Y piece of cloth so that the products made from the resulting pieces give the maximum sum of selling prices. You are free to make as many copies of a given product as you wish, or none if desired. How can i prove that the recursion is exponential and that dynamic programming is polynomial

The proof that recursion is exponential and that dynamic programming is polynomial is given by the formula;

P(x,y) = max{

P(x,y)

max (1 <= h <= X) { P[h, Y] + P(X - h, Y) }

max (1 <= v <= Y) { P[X, v] + P[X, Y - v] }

}

To prove that the recursion is exponential and that dynamic programming is polynomial. we will do so as follows;

Let us first have the assumption that the cloth is in such a manner that  either way, a product can be oriented. This implies that that after a cut, we will now have two pieces of cloth.

Now, we will make a list of the side lengths of the products that can fit in the piece after which we will consider a vertical cut for each of the side length as well as a horizontal cut for each of the side length, then we apply the same algorithm to each of the two resulting pieces.  

Thus, after the point above, it is likely true that in some instances, there may be a place to cut that is not at a product side length. However, It might be better for us to make a list of lengths composed of one or more pieces side by side as long as the sum is less than the length of the side being considered.

Lastly, we would note that this recursive approach is not limited to just two -dimensional problems as It could also be applied to a single or more than two dimensions. A useful proof would be to prove it for one dimension, then assuming it is true for n dimensions, prove it is true for n + 1 dimensions.

Thus;

P(x,y) = max{

P(x,y)

max (1 <= h <= X) { P[h, Y] + P(X - h, Y) }

max (1 <= v <= Y) { P[X, v] + P[X, Y - v] }

}

Read more at; https://brainly.com/question/11665190

some roadways are tilted as they go around a turn. what is the purpose of this tilt?

Question 2 (1 point)
Technician A says Radial ply Tires are used for carrying a heavy Load. Technician B says that Bias Ply Tires are made with the Plies laid diagnally.Which Technician is correct?

a)Technician A
b)Technician B
c)Both A & B
d)Neither

Question
The CNC is the primary interface between the machine operator and the machine. Is this statement TRUE or FALSE?
True
False

kdjdjfjfhfj jdjrjfbbfbf(xmpqitexsy.)​

EverFi future smart pie chart
Bond: 20%
Mutual fund: 15%
Stock: 50%
Savngs account: 15%

water 1°C.
12. Force is measured in
in the SI metric system.

Which of the following is NOT a type of soil structure?

Hey answer quick for 20 points

Technician A says that all ATF (automatic transmission fluid)'s are interchangeable.
Technician B says that new ATF should be red or pink in color. Who is correct?
A only
B only
Both
Neither

Which cars are least likely to have catalytic converter stolen

A change in what component of microscopy influences the apparent size of the objects being viewed?.

an HV battery radiator has intake air routed through the cooling fins of the ____ or heat exchanger before it circulates over the battery packs

If the actual work is 0.85 MJ for a compressor, and the isentropic compressor work is 0.8 MJ, what is the isentropic compressor efficiency

Subject : SCIENCE

1. in a simple circuit, increasing the voltage will ______ the electric current

2. increasing the resistance will ________ the electric current
​

“We have to redo the deck we built last week,” Bennett tells his coworkers. “I just tested it, and it doesn’t hold the minimum weight that the county requires. We have to replace it even though the client likes it as is and fixing it will cost us money.” What type of behavior is this?

A.
needs-driven

B.
consumer-driven

C.
emotional

D.
ethical

8. The two-stroke engine must still complete all four stages of operation-it just does this in two piston strokes instead of
O A. two
O B. four
OC. one
O D. three

5. How is the hydrogen gas balloon different from the hot air balloon? explain this in terms of density

Many engines in FWD vehicles must be removed with the transmission still attached.
O a. True
O b. False

Question 9 (1 point)
In the Standard Automotive Tire Designation P205/65R 15 94 T, the ________ is 94.

a)Load Index
b)Tread Height
c)Speed Rating
d)Wheel Height

Question 8 (1 point)
In the Standard Automotive Tire Designation P205/65R 15 94 T, the "T" designates the Tires _______.

a)Aspect Ratio
b)Load Index
c)Speed Rating
d)Tread Width

Why does the compression-refrigeration cycle have a high-pressure side and a low-pressure side?


a.The pressure difference is the result of polar molecular alignment due to the intense magnetic field created by the compressor motor.


b.So the refrigerant can condense at a low pressure and temperature and evaporate at a high pressure and temperature


c.The pressure difference isn't intentionally created but is simply the result of circulating refrigerant within the compressor.


d.So the refrigerant can evaporate at a low pressure and temperature and condense at a high pressure and temperature

Sand is composed mostly of ____ and is used to make glass, bricks, and concrete for the construction of roads and buildings.

Both model building codes and NFPA __________ can be used to determine the type of construction used in a building.

Which of the following maintenance items helps to ensure the vehicles engine lasts as long as possible?

A) cabin air filter

B) tire rotation

C) oil change

D) all of the above

Tensile strength is the amount of force necessary to:

The _______ is an exhaust manifold made of mandrel-formed steel tubes that are equal in length and joined at a common collector.

Maintenance is performed to help ensure;

A) safety

B) longevity

C) reliability

D) all of the above

A forced-air heating system uses a system of ____ air ducts to deliver warm air to the conditioned spaces.

Mark has a baking tray with 24 muffins the muffins are arranged in 4 rows how many muffins are in each row

How do you earn Brainliest?