Question

Ents

Suppose a furniture builder has two models of a bookcase: standard and artisan. The standard
model requires 4 hours to assemble and 2 hours for finishing touches. The artisan model requires 2
hours to assemble and 2 hours for finishing touches. Based on their current staffing, they can
manage a maximum number of assembly hours available is 48 per day, and the maximum number
of finishing hours available is 44 per day.
Let x = the number of standard model bookcases produced per day and y = the number of artisan
model bookcases produced per day.
Write the system of inequalities that represents the maximum number of bookcases that can be
produced in one day.

Answer 1

48 ≥ 4x + 2y

44 ≥ 2x + 2y

First, we will look at assembling hours.

"The standard model requires 4 hours to assemble [and] the artisan model requires 2 hours to assemble"

We also know they have 48 hours per day for assembly, x is standard model and y is artisan model.

48 = 4x + 2y

Lastly, they do not need to make that many, but they can so we will use greater than or equal to.

48 ≥ 4x + 2y

Now let us look at finishing hours.

"The standard model requires ... 2 hours for finishing touches. The artisan model requires ... 2 hours for finishing touches."

We also know they have 44 hours per day for assembly, x is standard model and y is artisan model.

44 = 2x + 2y

Again, they do not need to make that many, but they can so we will use greater than or equal to.

44 ≥ 2x + 2y