The Situation: Suppose you're catering an event for $200$ guests. Each guest will get a $4$-ounce portion of asparagus. Your supplier sells $20$-pound cases of asparagus for $\$38.95.$
Huge Question #1: How much does one $4$-ounce portion of asparagus cost?
Huge Question #2: What is the total cost of the asparagus used for the event?
Huge Answer #1: Find the Cost Per Unit!
First, find how much it costs to prepare one ounce of asparagus.
Divide the cost by the total number of ounces purchased: $$CPU=\frac{\$38.95}{20 \mbox{ lb}} \cdot \frac{1 \mbox{ lb}}{16 \mbox{ oz}} \approx \frac{\$0.122}{1 \mbox{ oz}}$$
Awesome!
So now if we want to know how much a $4$-oz portion costs to prepare, we simply multiply by $12.2$ cents per ounce by $4$ ounces for a total of $48.6$ cents, or $49$ cents per $4$ ounce portion.
... yes?
What is Grumpy Cat Trying to Tell Us?
Grumpy Cat wants us to know that it takes about $7.1$ ounces of unfabricated asparagus to make $4$ ounces of prepared asparagus since $$APQ=\frac{EPQ}{Y\%}=\frac{4 \mbox{ oz}}{0.56}=7.1 \mbox{ oz}$$
Answer to Huge Question #1
If we pay $12.2$ cents we pay per ounce, and we use $7.1$ ounces to prepare a $4$-ounce edible portion, our cost per $4$-ounce portion is $12.2 \cdot 7.1= 86.62$, or $87$ cents per $4$-ounce edible portion.
Special Note: when calculating cost, we round up to the nearest whole cent.
Very Special Note #1
Note that the above calculation is simply the formula $$\mbox{Cost}=CPU \times APQ.$$
Very Special Note #2
When doing calculations, it is best to do the entire calculation at once and round off at the end to avoid cumulative round-off error. When in doubt, use the bridge method:
$\mbox{Cost}=$ $CPU$ $\times$ $APQ$ $=$ $\displaystyle \frac{\$38.95}{20 \mbox{ lb}}$ $\cdot$ $\displaystyle \frac{1 \mbox{ lb}}{16 \mbox{ oz}}$ $\cdot$ $\displaystyle \frac{4 \mbox{ oz}}{0.56}$ $\approx \$0.87$
This is how you need to do it for the homework.
$$%\mbox{Cost}=CPU \times APQ=\frac{\$38.95}{20 \mbox{ lb}} \cdot \frac{1 \mbox{ lb}}{16 \mbox{ oz}} \cdot \frac{ 200 \cdot 4 \mbox{ oz}}{0.56} \approx \$173.89$$ Answer to Huge Question #2
To determine the cost of serving $200$ guests, we multiply the cost per $4$-ounce portion by $200.$ On paper, and on your homework, you should do the following calculation:
$\mbox{Cost}=$ $CPU$ $\times$ $APQ$ $=$ $\displaystyle \frac{\$38.95}{20 \mbox{ lb}}$ $\cdot$ $\displaystyle \frac{1 \mbox{ lb}}{16 \mbox{ oz}}$ $\cdot$ $\displaystyle \frac{200 \cdot 4 \mbox{ oz}}{0.56}$ $\approx \$173.89$
Reminder #1: When calculating cost, we round up to the nearest whole cent.
General Process: Finding Cost
1) Find the cost per desired unit of the food item.
2) If a food item requires fabrication, use the yield percent to calculate the amount of unfabricated product needed (i.e. $APQ$) to prepare the desired portion (i.e. $EPQ$).
3) You will multiply both quantities obtained in items 1) and 2) above to get cost. Use the bridge method to combine these calculations into a single calculation to avoid cumulative round-off error.
Reminder: Again, the above is simply the formula $\mbox{Cost}=CPU \times APQ.$
Bonus Example
Chef has made $24$ Blueberry Crêpes for a party. Each crêpe contains $5$ ounces of cleaned blueberries. The yield percent for blueberries is $92$ percent. If Chef bought blueberries in season for $\$6.06$ per pound, what is the cost of the blueberries cost for the party?
Another Free Example!
You purchase a case of mangoes for $\$10.29.$ The case weighs $4.1$ kilograms. The recipe for Mango Gazpacho calls for $4$ cups of roughly chopped mango. The yield percent for mangoes is $68$ percent and $1$ cup of roughly chopped mango weighs $5.9$ ounces. How much will the mangoes for this recipe cost?