### Video Transcript

A baby food factory produces two
types of baby food. The first type contains two units
of vitamin A and three units of vitamin B per gram. The second type contains three
units of vitamin A and two units of vitamin B per gram. If a baby needs at least 100 units
of vitamin A and 120 units of vitamin B per day, state the system of inequalities
that describes the food that the baby must eat each day to meet these
requirements. Use π₯ to represent the mass of the
first type of baby food in grams and π¦ to represent the mass of the second type of
baby food in grams.

In this question, we are told that
a factory produces two types of baby food. We will let π₯ represent the mass
of the first type of baby food and π¦ represent the mass of the second type. Since these are masses given in
grams, we know that both π₯ and π¦ must be nonnegative. Therefore, π₯ is greater than or
equal to zero, and π¦ is greater than or equal to zero. We know that the first type of baby
food contains two units of vitamin A per gram and the second type contains three
units of vitamin A per gram. As weβre also told that a baby
needs at least 100 units of vitamin A per day, we know that two π₯ plus three π¦
must be greater than or equal to 100.

We can find a similar inequality
for vitamin B. The first type of baby food
contains three units, and the second type contains two units. As a baby requires 120 units of
vitamin B per day, we have three π₯ plus two π¦ is greater than or equal to 120. We can therefore conclude that we
have a system of four inequalities that describes the food that a baby must eat each
day. π₯ is greater than or equal to
zero, π¦ is greater than or equal to zero, two π₯ plus three π¦ is greater than or
equal to 100, and three π₯ plus two π¦ is greater than or equal to 120.