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.

Answer 1

If the company used rectangular prisms it would take 40 boxes (2400/60) to hold 2,400 pencils which would cost $20 (40 times 0.50). If they used cylindrical containers, they would need 30 containers (2400/80) for a total of $22.50 (30*0.75).

To minimize the cost the company should go with rectangular prisms as they are the most cost effective.

Answer 2

To minimize the cost, the packaging that should be used is the rectangular prism boxes.

How to solve the cost minimization

From the complete information, the pencils needed is 2400. The prism can hold 60 pencils. Therefore, the number of prisms needed will be:

= 2400/60 = 40 prisms

The total cost for the prism will be:

= $0.50 × 40

= $20

The cylinder can hold 80 pencils. Therefore, the numbers needed will be:

= 2400/80

= 30

The cost of the cylinders will be:

= 30 × $0.75

= $22.50

Therefore, it implies that to minimize the cost, the packaging that should be used is the rectangular prism boxes.

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