MILKSHAKES AND MATRIX
MULTIPLICATION - WORKSHEET
Libby sells banana milkshakes. She makes two types: regular and supreme. The ingredients
for the regular are 3 bananas, 3 cups of milk, 1 cup yoghurt and two tablespoons of syrup.
The ingredients for the supreme are 4 bananas, 2 cups of milk, 1 cup yoghurt and 3
tablespoons of syrup.
The ingredients for the milkshakes can be organised into a matrix as shown below.
Libby receives an order for 2 regular milkshakes and 3 supreme. This can also be organised
into a matrix.
The total amounts of ingredients that Libby needs for this order will be as follows
2 × 3 + 3 ×4 = 18 bananas
2 × 3 + 3 ×2 = 12 cups of milk
2 × 1 + 3 ×1 = 5 cups of yoghurt
2 × 2 + 3 ×3 = 13 tablespoons of syrup
This calculation could be carried out using matrix multiplication:
3
[2 3] [
4
3 1 2
] = [(2 × 3 + 3 × 4) (2 × 3 + 3 × 2) (2 × 1 + 3 × 1) (2 × 2 + 3 × 3)]
2 1 3
= [18 12 5 13]
Matrix multiplication can be even more useful if there are several orders. Suppose Libby
receives the following orders:
Matrix multiplication can be used to calculate the amount of ingredients she needs for
each order:
2 3
3 3
[ 1 5] [
4 2
4 1
Note:
18 12 5 13
1 2
] = [23 13 6 17]
1 3
16 14 5 11
By adding up the
columns Libby can find
the total amount of
ingredients for all
the orders
Can you see the patterns that make this matrix multiplication
possible?
[3 rows and 2 columns] × [2 rows and 4 columns] = [3
rows and 4 columns]
MILKSHAKES AND MATRIX
MULTIPLICATION - WORKSHEET
Questions
1. Libby receives the following orders for milkshakes:
3 regular and 2 supreme; 2 regular and 2 supreme; 0 regular and 5 supreme; 1 regular and
4 supreme
a) Use matrix multiplication to calculate the amount of ingredients required for each
order
b) Calculate the total amount of ingredients required to meet all the orders
2. Libby charges $4 for a regular milkshake and $5 for a supreme.
a) Use the matrices below to work out how much Libby should charge for each
order.
3
2
[
0
1
2
2 4
][ ]
5 5
4
b) How much should she charge in total for all the orders?
c) It costs Libby $2.50 to make a regular milkshake and $3.50 to make a supreme.
Use matrix multiplication to work out how much it costs Libby to make each
order.
d) How much does it cost Libby in total to make all the orders?
e) How much profit does Libby make in total?
f) How much should Libby charge for these milkshake orders if she would like to
increase her profit by 10%?
Answers
1 (a)
[[17,13,5,12],[14,10,4,10],[20,10,5,15],[19,11,5,14]]
(b) [[70,44,19,51]]
2 (a) $22, $18, $25, $24 (b) $89 (c) $14.50, $12,
$17.50, $16.50
(d) $60.05 (e) $28.50 (f) various answers are possible
MILKSHAKES AND MATRIX
MULTIPLICATION - WORKSHEET