# Worksheet: Application of Matrix Multiplication

In this worksheet, we will practice writing, expressing, and solving real-life applications using matrix multiplication and other matrix operations.

Q1:

The table below shows the number of different types of rooms in three hotels in Hurghada which are owned by the same company. Given that a single room costs 350 pounds per night, a double room costs 450 pounds per night, and a suite costs 720 pounds per night, write a product of matrices that expresses the company’s daily income when all the rooms are occupied.

Hotel Single Room Double Room Suite
Venus 57 71 21
Pearl 30 77 27
Diamond 33 88 30

• A
• B
• C
• D

Q2:

The table below shows the number of different types of rooms in three hotels owned by a company. If a single room costs 160 LE per night, a double room costs 430 LE per night, and a suite costs 740 LE per night, determine the company’s daily income when all the rooms are occupied.

Hotel Single Room Double Room Suite
First Hotel 45 74 15
Second Hotel 48 74 19
Third Hotel 49 94 10
• A
• B
• C
• D

Q3:

The weight, in kilograms, of meat, vegetables, and fruit used to prepare lunch and dinner in a restaurant is shown in the table below. The restaurant buys one kilogram of meat for , one kilogram of vegetables for , and one kilogram of fruit for . Use matrix multiplication to find the total cost of the ingredients used to prepare each meal.

Meal Meat Vegetables Fruits
Lunch 180 120 130
Dinner 110 50 70
• AThe total cost of the ingredients used for lunch was , and the total cost of the ingredients used to prepare dinner was .
• BThe total cost of the ingredients used for lunch was , and the total cost of the ingredients used to prepare dinner was .
• CThe total cost of the ingredients used for lunch was , and the total cost of the ingredients used to prepare dinner was .
• DThe total cost of the ingredients used for lunch was , and the total cost of the ingredients used to prepare dinner was .

Q4:

A company has two offices, labeled and , in a town suffering an outbreak of influenza.

There are 120 male and 80 female employees at office and 60 male and 100 female employees at office . Represent this information as a matrix whose rows represent offices and , in that order, and whose columns represent the number of male and female employees, in that order.

• A
• B
• C
• D
• E

Currently, approximately of employees at and of those at are uninfected, of employees at and of those at are sick, and of employees at and of those at are carrying the virus. Represent this information as a matrix whose columns, in order, represent and and whose rows, in order, represent the proportion of employees who are uninfected, sick, or carrying the virus.

• A
• B
• C
• D
• E

Assuming that the proportion of employees who are uninfected, sick, and carriers in each office is the same for both genders, which of the following matrices represents the total number of male and female employees who are healthy, sick, or carrying the virus?

• A
• B
• C
• D
• E