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. o the rectangular prism boxes should be used because they will cost the company $2.50 less than using the cylindrical containers. o the cylindrical containers should be used because they will cost the company $2.50 less than using the rectangular boxes. o the rectangular prism boxes should be used because they will cost the company $5.00 less than using the cylindrical containers. o 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. o the rectangular prism boxes should be used because they will cost the company $2.50 less than using the cylindrical containers. o the cylindrical containers should be used because they will cost the company $2.50 less than using the rectangular boxes. o the rectangular prism boxes should be used because they will cost the company $5.00 less than using the cylindrical containers. o 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. Let $n_1$ be the number of rectangular - prism boxes. $n_1=\frac{2400}{60}=40$.

Step2: Calculate cost of rectangular - prism boxes

Each rectangular - prism box costs $0.50$. Let $C_1$ be 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. Let $n_2$ be the number of cylindrical containers. $n_2=\frac{2400}{80}=30$.

Step4: Calculate cost of cylindrical containers

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

Step5: Calculate cost difference

Let $\Delta C$ be the cost difference. $\Delta C=C_2 - C_1=22.5−20 = 2.5$. Since $C_1<C_2$, the rectangular - prism boxes cost less. The rectangular - prism boxes cost $2.5$ 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.