Costing/inventory models | Year 11

01 / LEARN

The idea, step by step

Connect quantities and prices

Quantity rows may represent stores and columns products. The price column must list the products in the same order. Multiplication adds quantity times price across products, producing one dollar total per store.

Keep quantities and prices separate to test price changes without replacing stock data. Check one row by hand before accepting a spreadsheet output.

Interpret assumptions

Prices can omit freight, GST, spoilage or bulk discounts. State what is included. To find closing stock, add deliveries to opening stock and subtract sales before valuing the result.

A negative physical count is a warning to reconcile records. Check timing, unrecorded deliveries and repeated sales deductions. Do not silently replace an impossible answer by zero.

A common trap

Prices can be in any order.

Instead: Price rows must match quantity columns.

02 / WORKED EXAMPLES

See the thinking

Example 1

Cost two orders

Notebook/pen quantities are $Q = (\begin{array}{cccccccccc} 3 & 2 \\ 1 & 4 \end{array})$ and prices $P = (\begin{array}{cccccccccc} 5 \\ 8 \end{array})$ dollars. Find costs.

First: $3 (5) + 2 (8) = 31$ .
Second: $1 (5) + 4 (8) = 37$ .

Q P = (\begin{array}{cccccccccc} 31 \\ 37 \end{array})

dollars.

Example 2

Closing stock

Opening $S = (\begin{array}{cccccccccc} 5 & 8 \\ 7 & 4 \end{array})$ , deliveries $D = (\begin{array}{cccccccccc} 3 & 2 \\ 0 & 5 \end{array})$ and sales $R = (\begin{array}{cccccccccc} 4 & 3 \\ 2 & 6 \end{array})$ . Find closing stock.

Use $S + D - R$ .
Calculate each position.

(\begin{array}{cccccccccc} 4 & 7 \\ 5 & 3 \end{array})

Check your understanding

Find the cost $(\begin{array}{cccccccccc} 4 & 3 \end{array}) (\begin{array}{cccccccccc} 6 \\ 9 \end{array})$ dollars.

Show answer

51 dollars.

$4 (6) + 3 (9) = 51$ .

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find order costs for $Q = (\begin{array}{cccccccccc} 2 & 5 \\ 4 & 1 \end{array})$ and $P = (\begin{array}{cccccccccc} 7 \\ 3 \end{array})$ .
2 marks
Stock is $(\begin{array}{cccccccccc} 20 \\ 15 \\ 8 \end{array})$ and sales $(\begin{array}{cccccccccc} 7 \\ 4 \\ 3 \end{array})$ . Find remaining stock.
2 marks
A quantity matrix has 3 shop rows and 4 product columns. What order must a price column have?
2 marks
Three items priced $p$ dollars each and two items priced 4 dollars each cost 29 dollars. Find $p$ .
2 marks
A stock calculation returns −2 items. Give a sensible response.
2 marks
A subtotal of 80 dollars attracts a uniform 10% delivery surcharge. Find the total.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find order costs for $Q = (\begin{array}{cccccccccc} 2 & 5 \\ 4 & 1 \end{array})$ and $P = (\begin{array}{cccccccccc} 7 \\ 3 \end{array})$ .
2 marks
$2 (7) + 5 (3) = 29$ .
$4 (7) + 1 (3) = 31$ .
$(\begin{array}{cccccccccc} 29 \\ 31 \end{array})$ dollars.
Stock is $(\begin{array}{cccccccccc} 20 \\ 15 \\ 8 \end{array})$ and sales $(\begin{array}{cccccccccc} 7 \\ 4 \\ 3 \end{array})$ . Find remaining stock.
2 marks
Subtract each sold count.
$20 - 7 = 13$ , $15 - 4 = 11$ , $8 - 3 = 5$ .
$(\begin{array}{cccccccccc} 13 \\ 11 \\ 5 \end{array})$ .
A quantity matrix has 3 shop rows and 4 product columns. What order must a price column have?
2 marks
Four rows match the products.
One column produces one cost per shop.
$4 \times 1$ .
Three items priced $p$ dollars each and two items priced 4 dollars each cost 29 dollars. Find $p$ .
2 marks
$3 p + 8 = 29$ .
$p = 21 / 3 = 7$ .
7 dollars.
A stock calculation returns −2 items. Give a sensible response.
2 marks
A negative count is impossible.
Check deliveries, sales and subtraction order.
Reconcile the records before reporting stock.
A subtotal of 80 dollars attracts a uniform 10% delivery surcharge. Find the total.
2 marks
The surcharge is $0.10 (80) = 8$ dollars.
Add it once: $80 + 8 = 88$ .
88 dollars.

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics: matrices and networks. Original learning resources follow the approved Ascent Library chapter map.

Official curriculum source ↗

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