Cold Pea Soup

Ingredients
Can of peas
2 jalapenos
juice of 1 key lime
``1 tablespoon olive oil

Combine all in a blender and blend.

Calories 390
Calories from fat 133
Sodium 1206
Carbohydrates 51
Complex Carbohydrates 34
Protein 16

Another update on the original diet problem

Yesterday I did a quick cost update on Stigler's 1939 minimum cost diet recommendation (it was published in 1945 but based on 1939 prices).

An update of his study was published in 2002 (based on 1998 prices). Written by Susan Garner Garille and Saul I Gass it appeared as "Stigler's Diet Problem Revisited" in Operations Research, Jan 2001.

A review of the article is here.

The researchers updated the original data to reflect price changes, revised values of the RDA's, and current evaluations of the nutrient content of the 77 foods chosen by Stigler. The updated problem shows that the optimal solution diet for a 25-50 year old man consists, on a daily basis, of 1.31 cups of wheat flour, 1.32 cups of rolled oats, 16 fluid ounces of milk, 3.86 tablespoons of peanut butter, 7.28 tablespoons of lard, 0.0108 ounces of beef liver, 1.77 bananas, 0.0824 of an orange, 0.707 cup of shredded cabbage, 0.314 of a carrot, 0.387 of a potato, and 0.53 cup of pork and beans. The daily cost of this diet is $1.78.

These costs are actually higher than the estimates I made yesterday for the Stigler diet. But they updated the model with more restrictions than in the original model, which would tend to cause an increase in minimum cost.

Both diets provides servings from all six food groups established by the USDA: 1) fats, oils, and sweets group; 2) milk group; 3) meats and beans group; 4) vegetable group; 5) fruit group; and 6) grain product group.

Cost of subsistence at today's prices

In Stigler's 1945 Journal of Farm Economics article he gave a solution to the diet problem of minimizing costs subject to some lower bounds on nutrition and vitamin intake which gave a daily ration of just a little more than

1 lb of flour
1/7 can of evaporated milk
.3 lb of cabbage
1 oz spinach
3/4 lb navy beans (dried).

That's a lot of bisquit and beans but it actually sounds like a pretty tasty daily ration.

In 1939 prices that worked out to about 11c a day.

Today you can get a 5 pound bag of flour for about $2. I think the cans are smaller these days than in 1939 but a can of evaporated milk is about $1. Cabbage is 50c a pound and dried navy beans about $1.25 a pound. Spinach prices vary but I'll estimate that at $1 a pound.

So, at today's prices, the daily ration above would cost about $1.69 per day.

Cabbage nutritional information

Green Cabbage Nutritional Information

Serving size 1/12 med. head (84g)
Calories 25
Total Fat 0g
Sodium 25mg
Total Carbohydrate 6g
Dietary Fiber 2g
Protein 1g

% of U.S. RDA
Vitamin A 0%
Calcium 4%
Vitamin C 60%

There are 454 grams per pound. So, per pound, cabbage has
135 Calories
135 mg sodium
32.4 g carbohydrates
5.4 g protein
21.6% DMR Calcium
324% DMR VC

Evaporated Milk Nutritional information

(condensed milk is usually sweetened)



Off brand labels are available for about 96c per 12oz can. At 2tbsp per serving, that's about 12 servings (2 tablespoons is about 1 fluid ounce).

The Original Diet Problem

Over the last few days I've been looking at a linear program to model the development of a minimum carb diet with bounds on protein, calories, and fat[1] [2] [3}. I thought this would be a nice time to take a short look at the origins of the mathematics of diet construction.

The diet problem originally arose about the time of the beginnings of the human experience. But it wasn't until George Stigler published his article, "The Cost of Subsistence" in The Journal of Farm Economics in 1945.

Stigler developed a minimum cost diet containing at least minimum levels of calories, protein, calcium, iron, vitamin A, vitamin B₁, vitamin B₃, niacin, and vitamin C.

This model was developed during WWII, before anyone had figured out an algorithm to solve a linear optimization problem so Stigler used a heuristic solution methodology to come up with a minimum cost diet of wheat flour, evaporated milk, cabbage, spinach, and Navy Beans.

I could live on that.

Tomato Drink


Lettuce, green leaf, raw 0.5 cup
Lime, raw, 1
Pepper, jalapeno, 0.5 pepper
Tomato juice, canned, 1 cup

Preparation

Chop the raw ingredients and put into a blender with the tomato juice.


FOOD SUMMARY

Total calories. 67
Calories from fat 3 (less than 1 oz fat)
Sodium 214 mg
Carbohydrates 18 g
Calories from carbohydrates
Protein 3g

NUTRITIONAL TARGET MAP™ The Nutritional Target Map™ allows you to see at a glance how foods line up with your nutritional and weight-management goals. The closer a food is to the right edge of the map, the more essential nutrients per calorie it contains. For a more nutritious diet, select foods that fall on the right half of the map.

The closer a food is to the top edge of the map, the more likely it is to fill you up with fewer calories. If you want to restrict your caloric intake without feeling hungry, choose foods from the top half of the map.

Foods that are close to the bottom edge are more calorie-dense. If you want to increase your calorie intake without getting too full, choose foods from the bottom half of the map.
Read more about the Nutritional Target Map

4.5 4.6 Fullness Factor ND Rating

NutritionData's Nutrition Data's Opinion
Opinion

NUTRITION DATA'S OPINION Nutrition Data awards foods 0 to 5 stars in each of three categories, based on their nutrient density (ND Rating) and their satiating effect (Fullness Factor™). Foods that are both nutritious and filling are considered better choices for weight loss. Foods that are nutritious without being filling are considered better choices for healthy weight gain. Foods that have more essential nutrients per calorie are considered better choices for optimum health.

Nutrition Data also indicates whether a food is particularly high or low in various nutrients, according to the dietary recommendations of the FDA.
Read more about Nutrition Data's opinion
Weight loss:
Optimum health:
Weight gain:

The good: This food is very low in Saturated Fat and Cholesterol. It is also a good source of Dietary Fiber, Thiamin, Niacin, Pantothenic Acid, Iron, Magnesium, Copper and Manganese, and a very good source of Vitamin A, Vitamin C, Vitamin K, Vitamin B6, Folate and Potassium.

The bad: This food is high in Sodium, and a large portion of the calories in this food come from sugars.
Caloric Ratio Pyramid Estimated Glycemic Load

CALORIC RATIO PYRAMID™ This graphic shows you what percentage of the calories in a food come from carbohydrates, fats, proteins, and alcohol. If you are trying to achieve a specific distribution of calories, such as the 40/30/30 distribution of the Zone™ diet, or the more traditional 60/30/10 distribution, the Caloric Ratio Pyramid™ will show you how recipes, meal plans, or individual foods line up with those goals.

Foods low in fat, for example, will cluster along the bottom edge of the pyramid, ranging from foods that are high in carbohydrates (at the left edge) to foods that are high in protein (at the right edge). Foods low in carbohydrates will cluster along the right edge of the pyramid, with foods that are high in fat at the upper edge and foods that are high in protein at the lower edge. Foods that have roughly the same number of calories from fats, calories, and protein will be found closer to the center of the pyramid.
Read more about the Caloric Ratio Pyramid

85% 5% 10%
Carbs Fats Protein

5
72
mildly anti-inflammatory
Estimated Glycemic Load


Inflammation Factor



ESTIMATED GLYCEMIC LOAD™ Glycemic load is a way of expressing a food or meal's effect on blood-sugar levels. Nutrition Data’s patent-pending Estimated Glycemic Load™ (eGL) is available for every food in the database as well as for custom foods, meals, and recipes in your Pantry.

How to interpret the values: Experts vary on their recommendations for what your total glycemic load should be each day. A typical target for total Estimated Glycemic Load is 100 or less per day. If you have diabetes or metabolic syndrome, you might want to aim a little lower. If you are not overweight and are physically active, a little higher is acceptable.
Read more about the eGL

IF (INFLAMMATION FACTOR) RATING™ The IF (Inflammation Factor) Rating™ estimates the inflammatory or anti-inflammatory potential of individual foods or combinations of foods by calculating the net effect of different nutritional factors, such as fatty acids, antioxidants, and glycemic impact.

How to interpret the values: Foods with positive IF Ratings are considered anti-inflammatory, and those with negative IF Ratings are considered inflammatory. The higher the number, the stronger the effect. The goal is to balance negative foods with positive foods so that the combined rating for all foods eaten in a single day is positive.
Read more about the IF Rating

Back to the diet problem

I’m still working on that linear programming model of a low carb diet.

Here’s my most recent solution

Carbohydtrates 3.19 grams

Food selections
yogurt 4
caulwsauce 3
banana 5.23
coffee 2
spinaprsalad 5
chili 0.18
AtkinsShake 0.49
Oatmeal 3

Protein 95
Calories 1800
Calories from fat 220

Note that I’ve added a few foods to select from and I’ve put some limits on how much of certain foods are selected. No more than 4 yogurts, 3 of the cauliflower w/cheese sauce, 2 coffees, 5 salads, and 3 oatmeals.

Foods in the mix that the model does not select are peanut butter w/cracker, tomato juice, and scrambled egg.

I’m still working on adding some foods to the model. Three that come to mind right now are bread, apricots, and maybe a shrimp salad.

The model likes the bread. Adding these three foods gives me a reduction in carbs from 319 g. to 291 grams but it means eating 18 hunks of Italian bread to get there. Limiting bread to 4 servings a day gives a more rational solution.except it calls for eating 28 apricots a day. Sigh.

I have three foods to select form with apricots (the shrimp salad, the spinach salad and the canned apricots). Limiting the combination of those three to a total of five apricots per day gives

Yogurt 4
Cauliflower 3
Banana 5
Coffee 2
Spinach/apricot salad 5
Chili 1.3
Bread 4

With 312 g carbs, less than 95 g. protein, 1800 calories, 220 from fat.

Shrimp and apricot salad

Kroger has a store brand of canned apricots that are sweetened with Splenda. The local store (Dillons) sells it for $2.09 for a 23.5 oz. bottle. Half cup servings have 30 calories, 7 g. of carbs. Cheap, nutritious, low carb, and tasty. I look for ways to eat it.

This shrimp salad is one way I came up with.

Makes 4 servings.

1 can tiny shrimp
6 canned apricot halves, chopped
1 stalk celery, chopped
1 cucumber, peeled and chopped
5 sprigs dill, chopped
4 green union stalks, chopped

Mix and toss ingredients.

According to this site, each serving has 224 calories (22 from fat), 30 g. protein, and 21 g. carbs.

Still more on the diet problem

The last couple of days I’ve been working on developing a linear programming model for a minimum carbohydrate diet that meets some restrictions on protein, calories, fat, and cost.

Yesterday I’d found a three food solution of
yogurt 5.6
cauliflower w/cheese sauce 9.5
banana 8.3
coffee 1

I guess that’s four foods if you count the cup of coffee.

Let’s add a couple of foods to the pool of foods for the model to choose from.

A spinach and apricot salad has 49 calories, none from fat, 12 g. of carbs and 2 g. of protein.

But that’s not really what I need to add to the mix. I need to find a high fat, low carb food to select from. Let’s try chili -- 194 calories, 68 from fat, 18 g. of carbs and 17 g. of protein.

Now we get a solution that looks like.

1 yogurt 4.763448 0
2 caulwsauce 0 0.827936
3 peanutbuttercrack 0 111.4818
4 banana 0 0.164621
5 coffee 1.292776 0
6 tomatoejuice 0 1.296119
7 spinaprsalad 18.79003 0
8 chili 2.534787 0
No. Constraint Dual Value Activity (A*x)
1 maxprotein -1.15522 95
2 minprotein 0 77
3 calories 0 2200
4 calfromfat -0.5715 220
5 mincalories 0.298708 1800
6 cost -0.72499 15
7 coffee 0 1

Like the last solution, this one has 3 foods plus coffee. But unlike the last solution this one is really a 4 food solution. The model forces at least 1 cup of coffee a day (I’m addicted). But that constraint isn’t binding in this solution, the optimal calls for 1.3 cups of coffee, more than the minimum.

The four constraints that are binding is the maximum limit on protein, the minimum level of calories, the maximum total cost, and the maximum number of calories from fat.

And although it’s a nice salad, almost 19 servings of the spinach/apricot salad a day isn’t really a satisfactory solution. Tomorrow I’ll add a couple new foods and look at some of the item costs more carefully.

More on the diet problem

Yesterday I started a linear programming formulation of the diet problem to minimize carbohydrate intake with constraints on calories, protein, and calories from fat. I gave three food solution to that three constraint problem. Today I want to extend that a little to more foods by adding some constraints.

The specific model I looked at yesterday was to minimize carbohydrates subject to calories between 1800 and 2200, protein between 77 and 95 grams, and calories from fat less than 220.by picking from CarbWatch yogurt, a cracker w/peanut butter, frozen cauliflower w/ low fat cheese sauce, and banana.

The 3 food solution was 5 yogurts, 6 bananas, and 14 servings of the cauliflower per day.

Let’s add a cost constraint of no more than $15 per day. The yogurt is 44c each, the cauliflower is $1 each. a banana is 30c, and a cracker w/ peanut butter is about 25c.

Let’s also add some foods. Add coffee, with a minimum of a cup a day. Also add tomato juice. Coffee has 5 calories (none from fat), .20 grams of protein and .90 grams of carb. Amost water. I estimate cost at about 25c per cup. A cup of tomato juice has 40 calories, 2 grams of protein and 10 grams of carbs. Cost is about 50c.

Adding the cost constraint gives a solution with less cauliflower and more yogurt and bananas.

Number of variables: 6.
Number of constraints: 7.
Minimization of objective function.

Primary objective function value: 3.18337136949888E+02
Dual objective function value: 3.18337136949887E+02
No. Name Value Reduced Cost Description
1 yogurt 5.618047 0
2 caulwsauce 9.532569 0
3 peanutbuttercrack 0 82.76391
4 banana 8.318303 0
5 coffee 1 0
6 tomatoejuice 0 3.546323
No. Constraint Dual Value Activity (A*x) Relaxation |b - A*x|
1 maxprotein -1.42217 95 0
2 minprotein 0 77 0
3 calories 0 2200 0
4 calfromfat 0 220 0
5 mincalories 0.287585 1800 0
6 cost -4.41075 15 0
7 coffee 1.951885 1 0

Although this says we have 7 constraints, the number of constraints that matters is the number of binding constraints. In our case we can have at most 5 binding constraints since we have separate constraints for upper and lower limits on protein and calories. In our minimum barbohydrate solution we are pushing the upper limi on protein and the lower limit on calories and are not binding on our limit on calories from fat. That suggests we need a diet with more fat in it. So I need to add some low carb, high fat foods to select from. I’ll do that tomorrow.

Simple spinach and apricot salad

1/2 cup raw spinich
2 chopped apricots.

Mix

Sprinkle with the juice of 1 lime.

The diet problem

I want to limit my carbs, my calories, my fat, and my protein, but I don’t want to starve to death.

One way to look at it is to minimize carbohydrates subject to calories between 1800 and 2200, protein between 77 and 95 grams, and calories from fat less than 220.

That’s a linear program, which I know how to solve. All that’s left to specify is the characteristics of the foods I want to pick from.

Let’s start with Kroger brand CarbWatch yogurt (not really a yogurt). It has 80 calories, 10 from fat, 12 grams of protein and 4 grams of carbs.

A diet of just the low carb yogurt won’t work, it has an infeasible solution to the linear program since to get enough calories from just the one food would greatly exceed my protein limits.

So as a second food I need to add something with very small protein contents. Let’s try a banana. That has 93 calories, 4+ from fat, 1 gram of protein, and 24 grams of carbohydrates..

About 6-7 yogurt containers and 13-14 bananas seems to be a workable mix although I think I’d tire of that diet pretty quickly and I expect that it would cause some deficiencies in vitamins my model isn’t tracking.

To add a little variety let’s think about a spoon full of peanut butter now and then, maybe on a cracker. One cracker with a tablespoon of peanut butter has 99 calories, 65 from fat, 24 grams of protein and 76 of carbs. Adding it still results in a two food solution.

One quirk of linear programming models is that an optimal solution will have no more than m nonzero food quantities if there are m restrictions on the model. My model has restrictions on calories, protein, and calories from fat so the model has room for at most 3 food choices. The three I’ve put into the model aren’t the right 3 to provide a mix though. Let’s try some more.

Kroger store brand has a frozen cauliflower side dish with a low fat cheese sauce., 60 calories, 10 from fat, 2 grams of protein and 10 grams of carbs. Adding that to my mix of food to pick from gives me a 3 food solution, 5 containers of the carbwatch yogurt, 6 bananas and 14 servings of the cauliflower with low fat cheese sauce.

Again, not a daily diet I’m going to look forward to. I like cauliflower, but 14 packages a day is a little much.

To get a 4 food solution I’m going to need a model with at least 4 constraints, in addition to adding more foods to pick from. I'll work on that tomorrow.

Tracking Diet

I'm having kidney problems, so I need to limit my protein intake. Because of diabetes I need to be careful with my carbohydrate intake. I need to lose weight so I need to limit my fat consumption.

It's quite a juggling act to do all that and still actually eat enough to stay alive.

More exercise would help but I'm limited in that right now also because I have some arterial blockages that cause a lack of stamina, shortness of breath.

Teeth and Sugar

As I mentioned in another blog posting, I recently discovered that I wasn't going to have to get a payday loan to pay for some new teeth, I'm able to get the VA to pay for it.

My teeth got in pretty bad shape after I developed diabetes. The first step in getting new dentures is to pull all your teeth. Then it takes the VA a couple of months to get the new dentures fitted and made. In the meantime I'm eating a lot of soup.

I was making with mostly just vegetables (I'm having kidney problems and am supposed to keep my protein intake low) and I wasn't putting any potatoes, noodles, or rice in the soups because of carbs.

The result has been that I've had a couple of t hose diabetic low carb attacks I'd always heard about but never experienced. Since I don't take insulin I don't ever get too much insulin. But the soup diet caused me to end up unintentionally restricting my carb intake even more than usual. Too much it seems.

Learn the signs of low blood sugar.