a company needs to package 2,400 pencils. a box in the shape of a rectangular prism can hold 60 pencils. a…

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 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 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 $5.00 less than using the rectangular boxes.

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 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 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 $5.00 less than using the rectangular boxes.

Answer

Explanation:

Step1: Calculate number of rectangular - prism boxes

To find the number of rectangular - prism boxes needed, divide the total number of pencils by the number of pencils each box can hold. The total number of pencils is 2400 and each rectangular - prism box can hold 60 pencils. So, the number of boxes $n_1=\frac{2400}{60}=40$.

Step2: Calculate cost of rectangular - prism boxes

Each rectangular - prism box costs $0.50. So the total cost of rectangular - prism boxes $C_1 = 40\times0.50=$20$.

Step3: Calculate number of cylindrical containers

To find the number of cylindrical containers needed, divide the total number of pencils by the number of pencils each container can hold. The total number of pencils is 2400 and each cylindrical container can hold 80 pencils. So, the number of containers $n_2=\frac{2400}{80}=30$.

Step4: Calculate cost of cylindrical containers

Each cylindrical container costs $0.75. So the total cost of cylindrical containers $C_2=30\times0.75 = $22.5$.

Step5: Calculate cost difference

Find the difference in cost $\Delta C=C_2 - C_1=22.5−20=$2.5$. Since $C_1<C_2$, the rectangular - prism boxes cost $2.50 less than the cylindrical containers.

Answer:

The rectangular prism boxes should be used because they will cost the company $2.50 less than using the cylindrical containers.