Fighting Off The Fog

Ugh-oh. Today my brain fogged up in hospitality math class. NOT a good sign.

I'll let the meat purchasing and costing problem on our class handout speak for itself:

A 15 1b. 11 oz. pork loin is purchased at $1.37 per lb. If 2 lbs. 4 oz. is removed by boning before cooking, 18 percent of the weight is lost due to roasting and another 9 oz. is lost in trimming and portioning, how much does a 6 oz. portion cost??

Yeah, I had to fight the temptation to yell out, "WHO CARES? LET THEM EAT CAKE!" 

But after I fought off the panic, and cleared away the fog, here's my best guess on how to solve this multi-part problem.  I'm guessing there's a 80 percent chance I've got it right. Anyone wanna take a bet on those odds? ;-)

My steps for solving this sucker:

1)  let's take care of the math parts that are easy. 15 lb. 11 oz. minus the 2 lb.  4 oz. lost in boning equals 13 lb. 7 oz. 

2) let's get that deboned, uncooked weight down to just ounces. We do that by dividing the 7 oz. by 16 (because there are 16 ounces in a pound), add the 13 lb. and multiply by 16 (to turn those pounds into ounces) to get a final oz. amount of 215 oz.

3) next, let's get rid of that 18 percent loss after roasting. 215 oz. minus 18 percent gives us our cooked weight of 176.3 oz. 

4) now let's minus the 9 oz. lost in trimming and portioning. 176.3 oz. minus 9 oz. equals 167.3 oz. (let's double check that this number is smaller than our original pork loin of 15 lb. 11 oz. Dividing our total 167.3 oz. again by 16 to turn them into pounds, we get a total cooked pound rate of 10.45625 lb. (or 10 lb. 7.3 oz.). So far, we've lost 5 lb. 3.7 oz. from our original loin.)

5) it looks like we're on track, so let's get to figuring out how much a 6 oz. portion costs. 167.3 oz divided by 6 oz. tells us that we can get 27.883333 portions out of our cooked loin. But in portioning, you always round down, as you can't serve up that .883333 portion. So we end up with just 27 portions.

6) to find the cost of a 6 oz. portion, we need to know how much we spent on our original 15 lb. 11 oz. loin. We're told we spent $1.37 per lb. So let's turn the 15 lb. 11 oz. into a decimal, so that our terms match. We do this by carrying the 15 lb. and multiplying the ounces by 16 to get 15.6875 lb. So, 15.6875 multiplied by $1.37 per lb. equals $21.50 for our original loin purchase.

7) we FINALLY get to that 6 oz. portion cost by dividing the total cost by the number of portions. So, $21.50 divided by 27 portions equals $0.7962962 per portion, or $0.796, as we typically carry the number to the third place.

Whew! Any chef, restaurant owner, or baker that can pound these types of calculations out quickly has my utmost respect!!

Onward and upward.  ;-)