Food Service Equations: Portion Costs

I like math.  Correction; I like easy math.  I am eternally grateful the applied nutrition curriculum's highest level of required math was pre-calculus.  I aced my pre-calc classes with A+'s, mostly because it's pretty simple math.  My method of studying when it came to math was to do example problems over and over until the process was brutally ingrained into my brain.  Sometime I understood what I was doing, and other times I didn't understand.  In those circumstances I repeated the example problem over and over until I could automatically and basically thoughtlessly solve the problem.  I think there is a lot more thinking involved with higher level calculus; thank God I dodged that bullet or I would probably have a life sentence at Cal Poly trying to get through math.

Anyways, I was studying for the DTR and hit the math problems: Food Cost Percentages; Edible Cost/Portion and Edible Yield; Cost Factor; Meals/labor hours, min/meal, payroll cost/day, payroll cost/meal, labor cost.  If you remember from my previous post about food service systems, I didn't pay much attention in my food service classes because I seriously underestimated an RD's role within the system itself.  (If you didn't read that one, long story short I assumed RD's lived in Clinical La La Land and had nothing to do with food service.  Some RD's might not be as involved with food service as others in the system, however they still must thoroughly understand food service.)

Anyways-anyways, I decided to take the same approach I did with pre-calc studying for the food service math problems and equations.  I kinda just did the problems and hoped it would stick.  I've been doing that on and off since July and nothing has stuck.  I decided to suck it up and actually learn the equations and why they were being used.  I want this information to stick with me so I can use it.  This requires me to teach myself using my study guide and the Internet since I never really comprehended it during my food service classes (shocking).  If I'm teaching myself, I might as well teach anyone reading this.  They say when you are able to teach someone else a topic it shows you fully comprehend it.  So, here we go!

Standard Portion Cost  (how much an item costs to purchase, prepare, and present)

These methods are used to help determine the total cost of product needed to produce an item on the menu. 

• Cost per unit is basically the cost of one portion from the whole unit.  This mostly has to do with items bought ready made, which is called the edible product in the food service world.  Basically, anything that can be served without altering (i.e. removing bones, cutting off stems).  Examples of edible products would include a cake that just needs to be sliced, a pack of bottled water, skinless/boneless chicken breasts, or pre-cut lettuce for salad.  Basically anything that requires little further prep before service.  

          To determine the standard portion cost, simply divide the cost of the whole unit by the

          number of portions.  For example, a cheesecake was purchased for $18 and can serve 

          12 people.  $18 by 12 servings equals $1.50 standard portion cost. This tells the kitchen

          how much each portion is costing them.  This can help determine how much an item

          should cost to the customer to make adequate profit for the business. 

• Yield calculations are used to determine how much of a product is used and how much it costs.  Most products are bought as purchased.  This is different than the edible product.  Products that are as purchased need further preparation.  This would include whole heads of broccoli (needs to be trimmed) or meat with skin/bones/fat that needs to be removed.  Or think about a bell pepper.  Lots of cutting and trimming.  Items such as these have trim loss or waste.  For example, you might need to buy 24 lbs of carrots.  However you cut 2 lbs worth of stems off (2 lbs of waste or 8.3% waste loss) and are left with 22 lbs edible portion (91.7% edible product).  

          If you take the edible weight and divide it by the as purchased weight and multiply by 100,

          you get the edible yield percentage.  Let's look at the green bean example:

          22 lbs / 24 lbs x 100= 91.7% edible yield

     

         If you flip flop that and take the as purchased and divide it by the edible portion, you can 

         see the percentage of edible cost.

         24 lbs / 22 lbs x 100= 109% edible cost or in decimal form, 1.09, also known as the cost 

         factor.

       

        **It's also important to remember that a buyer might look at the edible portion and compare

           that cost to the cost of a ready made product.  Keeping in mind labor costs, a buyer

           might decide a ready made product could be more cost effective after looking at the 
           edible portion from the as purchased.

Did I lose you?  I hope not.  Let's look at some sample problems and see if we can apply the terms and concepts learned.  (These sample problems are taken from a study guide I am using written by Jonathon Brown)

You need to prepare 374 4 oz portions of broccoli.  You note broccoli has a waste of 19%.  How much broccoli do you need to purchase?
Did you say 1,496 oz or 93.5 lbs?  If you did, you were thinking of the edible portion, not the as purchased amount.  

Did you get 115.5 lbs? Good job!
100%-19% waste=81% edible product
4 oz (portion size) divided by .81=4.938 oz (this is the AP amount per each portion)
4.938 divided by 16= 0.308 lbs
0.308 lbs x 374 servings= 115.5 lbs, round up to 116 lbs

OR make a proportion
81/100 (edible portion over total) cross multiply with 93.5 lbs/X (total edible portion over the variable, the total as purchased)
(81)(X)=(100)(93.5)
81X=9350
X=115.5 lbs


The yield factor on green cabbage is 87%.  Approximately how much cabbage is needed to prepare 175 servings of coleslaw that requires 2.25 oz of cabbage in each serving?
This is similar to the broccoli question.  87% edible portion is given and we are finding the amount in pounds that should be bought.  You could made a proportion again:
87/100 cross multiply with 24.61 lbs/X [24.61 lbs was found by (175)(2.25oz)]
X=28.3 lbs to purchase, round up to 29 lbs


You have purchased 35 lbs of fresh green beans with a 23% waste.  How many 4 oz portions will be prepared?
First let's figure out how many ounces are in 35 lbs.  35 lbs x 16 oz in a lb = 560 oz purchased

Second let's figure out the yield/edible portion (77%) of 560 oz.  560 oz x 0.77 = 431.2 oz

Lastly, divide 431.2 oz by 4 oz portion = 107.8 portions, 107 portions


How many pounds of pork roast (with a 15% shrinkage factor) should be bought to serve 600 portions that each weigh 3 oz?
First let's find out the total edible amount needed for service : 600 x 3 oz=1800 oz or 112.5 lbs

Next make a proportion again since we are trying to figure out how much to purchase
85/100 cross multiply with 112.5 lbs/X
(112.5)(100)=(85)(X)
11,250=85X
=132.35 lbs, round up to 133 lbs


CURVE BALL!  I'm going to throw in a scooper problem at you since I explained the concept in an earlier post (see Buckeyes).  The Standard portion for gravy is served with a No. 8 scoop.  Three gallons of the product should yield how many servings?
Do you remember what the number means?  It is the amount of scoops the scooper can get from 1 quart.  Therefore this scooper can get 8 scoops from 1 quart.  The question is asking how many scoops you could get from 3 gallons.

Since there are 4 quarts in 1 gallon, 3 gallons=12 quarts.  8 scoops x 12 quarts = 96 servings


A 4 oz serving of soy cheese is used in one omelet.  How many 5 lb blocks of cheese do you need to make 400 omelets?
1600 oz or 100 lbs are needed total.  100 lb divided by 5 lb blocks equals 20 blocks




Well that wasn't too bad now was it!  Stay tuned for more math adventures regarding Food Cost Percentages, Meals/Labor hrs, and Payroll Costs!