The next step is to add the decision variables
to the model. I added a row for the decision variables and gave it the
label Qty Produced (or Quantity Produced). In this problem, the
decision variables are the numbers of each chair to manufacture. I've
arranged these variables so they're aligned in the same columns as the
data on which they'll operate. (Click here
to see the entire worksheet at this stage.)
Since in August, OP always makes forty chairs of
each type, we fill the Qty Produced row with 40 for each chair.
I've highlighted these critical decision variable cells with a border
(explained below on formatting) to distinguish them from the data.
In our model we need to track how many of each chair
component we use. In our situation, components are a constrained quantity
since we can't use more than what the factory has on hand for the month
of August. We'll track that value for each chair component by means
of a Total Usage calculation.
Because of the way the data is arranged, we can save
time and effort and simplify the worksheet in our calculation of Total
Usage by using a builtin Excel function named SUMPRODUCT.
This function allows us to easily compute the Total Usage for
the first chair component (long dowel) for all six chair types.

Capt

Mate

AmHi

AmLo

Spank

SpanQ

Total
Usage

Long
Dowel

8

0

12

0

8

4

0

Then we can copy the formula we've built for the
first long dowel component so it calculates Total Usage for each
of the rest of the components (short dowel, leg, heavy seat, etc.).
The SUMPRODUCT function is a shorthand way to do
the following:
 Multiply the Qty Produced for the
Captain's chair by the number of long dowels needed for that model.
Then:
 Multiply the Qty Produced for the
Mate's chair by the number of long dowels needed for that model. Then:
 Do the same operation for the long dowel
component for each of the quantities produced for each of the remaining
four chair models: American High, American Low, Spanish King, and
Spanish Queen. Then:
 Add together the results for all the chair
models for Qty Produced X number of long dowel components required.
The result of this addition is the Total Usage, or the total
number of long dowels required for all the chairs.
The SUMPRODUCT function for the long dowel component
has this format:
=SUMPRODUCT($C$4:$H$4,C9:H9)
Or, an easiertounderstand version might look like
this:
=SUMPRODUCT(AllChairsQtytoProduceRange,AllChairsLongDowelRange)
In our example, this formula goes into the first
cell (Cell K9) in the Total Usage column. That is, in the row
for long dowel.
To summarize:
 $C$4:$H$4 is the range referring to the
quantities of each chair produced.
 C9:H9 is the range referring to the number
of long dowels required for each chair type.
Copy the formula for the long dowel down the Total
Usage column, to complete the formulas that are required for each
of the rest of the components.
Click here
to review an important note on the use of absolute and relative addressing
in the SUMPRODUCT formula used above.