#DailyBloggingChallenge (135/200)
Some times one questions how the price of an item was decided on. Like take for example pickles, there are multiple options at the store although they all have basically the same ingredients.
One could claim one is paying extra for the brand. That would be fine if the brand was actually good, though lots of times, I have found the no name brand or store brand is better than some specific big name brand.
#DailyBloggingChallenge (138/200)
Over the past two days, I was living off of 5min quick make foods meaning one just needs to add hot water, stir, and wait.
Each meal/cup had a dry weight of about 60g and ca 250g wet weight. And it would take about 3 cups to be satiated.
Considering that the price per cup ranged from 0.80-3.50€ and the convenience factor, it can be quite an expensive luxury, depending on what price tag one puts on one's own working time.
If one's working time cost is 0.00€, then one is looking at 10.50€ per meal. Now considering one would buy the raw ingredients, which would on average cost only a fraction of the price, then one quickly realizes the luxury of such quick convenience foods.
#DailyBloggingChallenge (139/200)
Let `p` be price of cup and `w` be hourly work cost. Then the cost `C` of preparation per cup is
```
C = p + w * t
```
for time `t` in hours.
If we take a look at the three cup example for satiation of a meal `M`.
```
M = 3 * C = 3 * (p + w * 0.083)
```
Let's take a look at various price points `p = {0.8, 1.5, 3.5}` and various hourly wages `w = {20, 50, 100}`. Then this gives us the table `WP`.
| w\p | 0.8 | 1.5 | 3.5 |
| ------ | ------- | ------- | -------- |
| 20 | 7.4 | 9.5 | 15.5 |
| 50 | 14.5 | 17 | 23 |
| 100 | 27.4 | 29.5 | 35.5 |
Now considering that whole food costs a fraction `p_f` of the price of convenience food, though in return needs more prep time `t_f`.
This gives us the new equation of
```
C_f = p_f * p + w * t * t_f
```
and
```
M_f = 3 * C_f = 3 * (p_f * p + w * t * t_f)
```
We will look at `p_f = {0.5, 0.8}` and `t_f = {5, 10}`; only on the last two columns of the previous table `WP`.
First we will multiply `p_f * p` and `t * t_f`, so that we can use the equation `M`.
Let table `P` be
| `p_f\p` | 1.5 | 3.5 |
| ---------------- | ------- | ------- |
| 0.5 | 0.75 | 1.75 |
| 0.8 | 1.2 | 2.8 |
and table `T` be
| `t_f\t` | 0.083 |
| ---------------- | --------- |
| 5 | 0.42 |
| 10 | 0.83 |
This give us the equation
```
M_f = 3 * C_f = 3 * (P + w * T)
```
and the table `WTF`
| `w\t_f` | 0.42 | 0.83 |
| ---------------- | -------- | ------- |
| 20 | 8.4 | 16.6 |
| 50 | 21 | 41.5 |
| 100 | 42 | 83 |
with this we can finally calculate the table `WPF`
| `w*t_f\p_f` | 0.75 | 1.2 | 1.75 | 2.8 |
| ------ | ------- | ------- | -------- |
| 8.4 | 27.45 | 28.8 | 30.45 | 33.6 |
| 16.6 | 52.5 | 53.85 | 55.5 | 58.65 |
| 21 | 65.25 | 66.6 | 68.25 | 71.4 |
| 42 | 130.5 | 131.85 | 133.5 | 136.65 |
| 83 | 251.25 | 252.6 | 254.25 | 257.4 |
since 41.5 and 42 are close, we omitted the prior one.
The table `WPF` shows that considering one's own wage price for food prep, then a meal becomes quite expensive.
So next time one complains how expensive a meal is at the #restaurant, one can compare how expensive it would be if one prepped it oneself.
#maths #cooking