Question

A manufacturer produces both two-slice and four-slice toasters. The two-slice toaster takes 6 hours of labor to produce and the four-slice toaster takes 10 hours. The labor available is limited to 300 hours per week. and the total production capacity is 40 toasters per week Part A: Write a system of inequalities to represent this scenario. (Hint: You should have 2 inequalities)

Answer 1

We have two products: a two-slice toaster and a four-slice toaster.

Lets call T the number of two-slice toasters produced and F the number of four-slice toasters produced.

If we have 300 hours per week of labor, the sum of the labor required for T and F has to be lower or equal to that value.

The labor hours that take to make the two-slice toasters can be written as 6*T, as it is the product of the hours per unit (6 hours/unit) by the number of units (T units).

The same can be done for F, where the labor required can be expressed as 10*T.

If we add these terms, and make them be less or equal than 300, we get:

$6T+10F\le300$

The production capacity is 40 units, so the sum of T and F has to be less or equal than 40.

We can express this as:

$T+F\le40$

Answer:

The system of inequalities for this problem becomes:

$\begin{gathered} 6T+10F\le300 \\ T+F\le40 \end{gathered}$

6T+10F<=300

T+F<=40