What if Pizza Hut salad collapses?

Analysis on Stacking Scheme of Pizza Salad Tower

By analyzing the stacking problem of Pizza Hut salad tower, this paper puts forward a scheme to maximize the volume of stacking salad tower, that is, spreading carrot strips radially on the outer edge of the dinner plate, stretching out nearly half the length as the bottom, then using pineapple blocks on the periphery as the load-bearing wall, placing favorite contents in the middle, and lifting them layer by layer to reach the ideal height and obtain the ideal volume. Finally, this paper gives the graphic strategy of stacking salad tower.

Pizza hut, salad tower

1 ask questions

PizzaHut has a buffet salad in 28 yuan. Put your favorite salad ingredients in an empty bowl. It is said that the buffet salad in Pizza Hut abroad can be added after eating, but there seems to be no such rule in China. Of course, the pursuit of as many patterns as possible is the goal of almost every consumer. This paper aims to explore how to achieve this goal and give reasonable and feasible methods.

2 problem analysis

Pursuing the maximization of code quality is an extreme problem.

The shape of the packaged salad tower is approximately a frustum. Assuming that the density of each material is similar, the frustum only needs to be particularly large.

3 model hypothesis

3. 1 Ignore the density difference of various materials;

Carrots and yellow peaches are not the same thing, and their densities are naturally different, but for the convenience of analysis, they are regarded as substances with the same density;

3.2 Ignore the gap between materials;

There are inevitably many holes between various materials. Although they can be filled with small particles such as raisins and corn kernels, there will still be many holes. Ignored here;

3.3 It is considered that the shape of Salata is frustum;

Because the interior of the board-that is, the volume from the plane where the edge of the board is located to the bottom of the board-is full of contents regardless of the stacking mode, this volume has the same contribution to different modes, so it is not considered;

The shape of the frustum of a cone, in popular terms, is the shape left after the cone is parallel to the bottom and the upper tip is cut off.

3.4 It is considered that radish strips are cubic cylinders with square cross sections;

For example, a cubic column with a square cross section is 0.5cm× 0.5cm×10cm.

4 model construction

Under the above assumptions, the vertical section of Shalata is shown in Figure 4- 1.

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Figure 4- 1 salad tower longitudinal section

The model is established as follows:

When the size of the plate (black part in Figure 4- 1) is fixed, the volume V of the salad tower (pink part in Figure 4- 1) is the largest. The objective function is:

Vmax

(4- 1)

5 model calculation

5. 1 volume calculation

Mark the size on Figure 4- 1 to get Figure 5- 1. HR2R 1Rγ

Fig. 5- 1 salad tower longitudinal section dimension drawing

As shown in figure 5- 1, r represents the outer edge radius of the plate, R 1 represents the upper bottom radius of the frustum, R2 represents the lower bottom radius of the frustum, h represents the height of the frustum, and γ represents the included angle shown.

According to the formula for calculating the volume of frustum of a cone, there are:

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)SSSS(3HV22 1 1++=

(5- 1)

Among them, 1S2S represents the area of the upper and lower surfaces of the frustum.

2 1 1RSπ=，222RSπ=

(5-2)

Substituting (5-2) for (5- 1), there is

)RRRR(3HV222 12 1++？ =π

(5-3)

This is the volume of the frustum of a cone. It can be seen from Equation (5-3) that when any value of,, and h increases, V will increase. 1R2R

Obviously, in the case of fixed sum, H is a linear factor, which conforms to the habit, that is, the higher the code, the larger the volume. When H is fixed, there are three relationships with * * *: 1R2R 1R2R.

1), as shown in figure 5-2 (a). This shape is relatively stable and easy to realize. 2 1RR & lt；

2), as shown in figure 5-2 (b). This shape is fairly stable, which is the limit case of 1). 2 1RR=

3), as shown in figure 5-2 (c). This shape is unstable and difficult to achieve. 2 1RR & gt；

(a)2 1RR & lt；

2 1RR=

(c) 2 1RR >

Figure 5-2 and 1R2R, the vertical section of Shalata.

From the point of view of easy operation, we don't consider case (c). Of course, (c) is not necessarily impossible, just because of poor operability. Once it collapses, it will be embarrassing!

To be on the safe side, here we choose case (a) and case (b) for discussion, that is, 2 1RR≤.

5.2 R2 maximization

Obviously, the key is how to maximize. In other words, under the condition that the radius r of the outer edge of the plate is constant, how to build the bottom layer with a large radius is the key to the huge salad tower. 2R2R

According to the actual situation, the optional "building materials" are: carrot sticks, pineapple pieces, yellow peach pieces, apple pieces, cucumber slices, salad dressing, corn kernels, green beans, green pepper rings (not available in some stores) and so on?

We use the longest carrot sticks as the bottom building materials. According to the hypothesis, radish strips are considered as cubic cylinders with square cross sections, as shown in Figure 5-3 (a). Its cross section is square, as shown in Figure 5-3 (b). The longitudinal section is rectangular, as shown in Figure 5-3 (c).

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Carrot strips

intersecting surface

(c) longitudinal section

Figure 5-3 Cross Section and Longitudinal Section of Carrot Strip

Carrot strips are placed radially, as shown in Figure 5-4 (a), with the roots connected and the outside extending out of the outer edge of the plate. The dimensions are shown in the figure. The green part is enlarged, as shown in Figure 5-4 (b).

(a) Top view with dimensions

(b) Partial expansion

Figure 5-4 Schematic Diagram of Carrot Strip Placement

According to the geometric relationship, the following equation holds:

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2sin2θ？ =rc

(5-4)

2tan2θ？ = research and development

(5-5)

θ? =re

(5-6)

When 0→θ, there is

θθθ~tan~sin

(5-7)

Because the actual θ is very small, it can be approximately considered that C, D and E are equal. The number n of carrot sticks that can be placed is:

drN/2π=

(5-8)

Let's look for the calculation expression of r, obviously:

Rrl=+2

(5-9)

Lll=+2 1

(5- 10)

Let k be the detection coefficient, then there are:

Llk/ 1=

(5- 1 1)

Replace, get:

LkRlLRlRr) 1(][ 12？ =? =? =

(5- 12)

So, there are:

]) 1([2LkRdN？ =π

(5- 13)

according to

2rl =+

(5- 14)

have

kLRR+=2

(5- 15)

Formula (5- 15) is an expression. 2R

Because to maximize, and both R and L are fixed values, it is necessary to maximize K, and the range of K is 0~ 1. According to the lever principle, radish strips can be stabilized in the tray. If K >: 0.5, radish strips will fall off the plate. Of course, you can press some materials on the radish strips to keep the balance when the k> is 0.5, but this kind of effort is easy to fail, which is not in line with our original intention of finding a simple and safe method, so we don't consider it. 2R5.0k≤

When k=0.5, the extreme value is 2R.

5L.0RRmax 2+=

(5- 16)

At this time, the number of radish strips is

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]5.0[2LRdN？ =π

(5- 17)

6 model verification

One day, I went to PizzaHut in Anzhen Hualian with Denver and Spring and asked for a buffet salad. Measurement parameters, the values are as follows:

R =16.8cm ÷ 2 = 8.4cm.

Length = 5.5 cm

D = 0.8 cm

Take k = 1/3 and calculate N = 37, which is actually exactly 37, as shown in Figure 6- 1, which is exactly the same!

Then put it layer by layer according to the above method. Because there were only three people, I didn't want to waste it, so I just built a six-story frustum and called it a day. The last three people ate for half a second, and the salad piled up in their throats and almost fell off?

Figure 6- 1 Schematic diagram of carrot sticks placement

7 graphic strategy

Photographer: IT migrant workers, Denver

Shooting time: 20041October 30th.

Location: Pizza Hut, Parkson Supermarket, Xueyuan Road

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Construction workers: IT migrant workers, Denver, Corso, A Mu.

I have to say something. I wonder how other Pizza Hut restaurants are doing. This time I went to the Pizza Hut in Parkson Supermarket on Xueyuan Road, and found that compared with the Pizza Hut in Anzhen Hualian last time, carrot strips were used as the base material and pineapple pieces were used as the load-bearing wall material, which obviously succeeded in losing weight! A serious BS!

No matter how much, let's start! Are you ready? Here we go.

7. 1 Wash your hands

Hands are the most dexterous. Wash up and get ready for work!

7.2 Empty pallets should be used as centralized pallets for building materials.

Be sure to ask the waiter for an empty plate to come to fashion building materials. This makes it convenient for many people to operate in parallel: one person selects materials with suitable shape and strength and puts them in the plate, while the other person grabs materials from the plate and piles them into salad towers.

7.3 Fill the bottom pit of the salad bowl.

What's your favorite food? I thought the yellow peaches were good, so I put a lot of yellow peaches in the bottom pit of the salad bowl, and also put some small cisse gaps such as corn kernels until it was close to the plane.

7.4 Stick radish strips on the edge of the salad bowl as a base according to radiation.

This is really important. High-rise buildings have sprung up, there is no solid foundation, and Salata is not practical. After analyzing several methods in the literature, radish strips were determined to be the most suitable substrate. Be sure to carefully select healthy and energetic radish strips of similar size! The elongation rate of radish strips is as close as possible to 0.5, which is proved to be reliable in practice. Radish strips are in contact at the bottom and scattered at the top in a radial shape, as shown in Figure 7- 1. In order to stick radish strips firmly, you need to use a proper amount of salad dressing as glue, and you should master this degree yourself.

Figure 7- 1 Radish strips for foundation construction

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Compare figure 6- 1 and figure 7- 1. Only 37 yuan for one, and 52 yuan for this one! Radish strips have shrunk so much! Moreover, there are no radish strips in the self-service salad area on the second floor of the Pizza Hut Store of Parkson Supermarket on Xueyuan Road! It's ~ ~ ~

7.5 Press the inner ring of radish strip foundation with pineapple pieces.

As shown in Figure 7-2, press the inner ring of the radish strip foundation with pineapple blocks to prevent the radish strip from falling off.

After the radish strips are laid, the pineapple pieces are used as load-bearing walls. Because it is strong enough and has a good cube shape, the friction force is large enough compared with the yellow peach block, and it is not as slippery as the yellow peach block. The selection principle of pineapple pieces is uniform, square and hard. There is also a lot of water because of the long soaking time. Under the weight of the above materials, the edge of the plate will ooze. Be careful not to drip on your clothes.

Once again, protest against the merchants not to cut the pineapple pieces too thin, which will seriously affect the construction mood of the construction workers!

Fig. 7-2 Pineapple block pressing radish strips in the inner ring.

7.6 Press the outer ring of radish strip foundation with pineapple pieces.

As shown in Figure 7-3, enlarge this circle as much as possible, and this is the bottom surface of Salata cylinder.

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Figure 7-3 Radish strips pressed on the outer circle of pineapple blocks.

7.7 Fill the pit surrounded by pineapple rings with favorite materials, and then cover with cucumber slices to create a perfect platform.

As shown in Figure 7-4, radish strips are used as the base, pineapple blocks are put in, cucumber slices are placed on the pineapple blocks, and the uneven top surface is ground flat. Usually 1~2 layers of cucumber slices are enough. What can't be done with such a perfect platform?

Figure 7-4 Building a platform with cucumber slices

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7.8 Surround the outer ring of the platform with pineapple blocks as load-bearing walls.

As shown in Figure 7-5, pineapple blocks as load-bearing walls must be selected with uniform heads, regular shapes and high strength.

Figure 7-5 Pineapple blocks surround the outer ring of the platform as a load-bearing wall.

7.9 Fill the load-bearing wall with favorite materials.

As shown in Figure 7-6, because pineapple pieces are unkind, the load-bearing wall is a double-layer pineapple piece, which requires more skills, because it will collapse if you are not careful. To be on the safe side, it is recommended to collect some inward. After that, fill the wall with your favorite materials. Three slices of cucumber is Theory of Three Represents's theory.

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Figure 7-6 Filling the load-bearing wall with favorite materials

7. 10 Another perfect platform

Figure 7-7 is the top view of the perfect platform, and Figure 7-8 is the side view of the perfect platform. Building a salad tower on such a perfect platform, I think only the sky is its limit.

Figure 7-7 Another Perfect Platform

Figure 7-8 Side of the Perfect Platform

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Before 7. 1 1 is about to be completed.

As shown in Figure 7-9, it is a pleasure to build a salad tower on such a perfect platform, but there are only four of us. In line with the principle of not wasting, take it as soon as possible, only take this high.

Figure 7-9 Before completion

7. 12 capping

Figure 7- 10 is the top view of the Salad Tower after it is capped. At least it's a tower. No one should have a problem with adding a sharp point, right?

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Figure 7- 10 Salad Tower is capped

Fig. 7- 1 1 is a side view. Yes, it's not high, but its bottom area is large enough. Not high, just because of the limitation of the sum of the stomach volumes of the three of us. If you like, it is no problem to triple your height now. As a demonstration of graphics course, the key steps have been clearly explained, which is enough.

Figure 7- 1 1 Salata side view

7. 13 Divide the dishes according to the head. Let's eat!

Ask the waiter for some empty plates and divide the salad tower carefully. There is nothing to say. Be careful, if I knock over the fruits of victory and get beaten, I have nothing to say.