Question

A company needs to package 2,400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box costs the company $0. 50, while each cylindrical container costs $0. 75. Which packaging should the company use to minimize cost? Explain. The rectangular prism boxes should be used because they will cost the company $2. 50 less than using the cylindrical containers. The cylindrical containers should be used because they will cost the company $2. 50 less than using the rectangular boxes. The rectangular prism boxes should be used because they will cost the company $5. 00 less than using the cylindrical containers. The cylindrical containers should be used because they will cost the company $5. 00 less than using the rectangular boxes.

Answer 1

The true statement is (a) The rectangular prism boxes should be used because they will cost the company $2. 50 less than using the cylindrical containers.

The given parameters are:

$Pencils = 2400$ --- the pencils needed

The number of pencils the prism can hold is:

$Prism =60$

Divide the number of pencils needed by the number of pencils in 1 rectangular prism, to calculate the number of prisms needed (n1)

$n_1 = \frac{Pencils}{Prism}$

So, we have:

$n_1 = \frac{2400}{60}$

$n_1 = 40$

A rectangular prism costs $0.50.

So, the total cost is:

$Total\ cost = 40 \times 0.50$

$Total\ cost = \ 20$

The number of pencils the cylinder can hold is:

$Cylinder=80$

Divide the number of pencils needed by the number of pencils in 1 cylinder box, to calculate the number of cylinders needed (n2)

$n_2 = \frac{Pencils}{Cylinder}$

So, we have:

$n_2 = \frac{2400}{80}$

$n_2 = 30$

A cylinder costs $0.75.

So, the total cost is:

$Total\ cost = 30 \times 0.75$

$Total\ cost = 22.5$

By comparison, the rectangular prism costs $2.5 less than the cylinder

Hence, the true statement is (a)

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