Question

5. For the following four machine parts, find W, the number of pounds per part; C, the cost of the metal per part; and T, the total cost.

Answer 1

Step 1: Let calculate the pounds (W) For machine part A

Given data

`\begin{gathered} \text{Number of inches n}eeded=\text{ 44.5} \\ Number\text{ of pounds per inch=0.38} \\ cost\text{ per pound = \$0.98} \end{gathered}`
`\begin{gathered} 1\text{ inch =0.38 pounds} \\ 44.5\text{ inches = 44.5 }*0.38 \\ 44.5\text{ inches =16.91 pounds} \end{gathered}`

The pounds ( W) for machine part A = 16.91 Pounds

Step 2: Let calculate the COST (C) For machine part A

`\begin{gathered} \text{Cost (C) = number of pounds }*\cos t\text{ per pound} \\ \cos t\text{ (c) =16.91 }*\text{ \$0.98} \\ \cos t\text{ (C) = \$16.57} \end{gathered}`

The cost of part A = $16.57

Step 3: Let calculate the pounds (W) For machine part B

Given data

`\begin{gathered} Number\text{ of inches n}eeded=122.0 \\ \text{Number of pounds per inch=}0.19 \\ \cos t\text{ per pound = \$0.89} \end{gathered}`
`\begin{gathered} 1\text{ inch =0.19 pounds} \\ 122.0\text{ inches = 122.0}*0.19 \\ 122.0\text{ inches=23.18 pound} \end{gathered}`

The pounds ( W) for machine part B = 23.18 Pounds

Step 4: Let calculate the COST (C) For machine part B

`\begin{gathered} \text{Cost (C) = number of pounds }*\cos t\text{ per pound} \\ \text{Cost (C) }=23.18\text{ Pounds}*\text{ \$0.89} \\ \text{Cost (C) }=\text{ \$20.63} \end{gathered}`

The cost of part B = $20.63

Step 5:Let calculate the pounds (W) For machine part C

Given data

`\begin{gathered} Number\text{ of inches=108.0} \\ \text{Number of pounds per inch= 0.08} \\ \cos t\text{ per pound = \$1.05} \end{gathered}`

`\begin{gathered} 1\text{ inch=0.08 pounds} \\ 108.0\text{inches= }108.0*\text{ 0.08} \\ 108.0\text{inches}=8.64\text{ pounds} \end{gathered}`

The pounds ( W) for machine part C = 8.64 Pounds

Step 6: Let calculate the COST (C) For machine part C

`\begin{gathered} \text{Cost ( C) = number of pounds }*\cos t\text{ per pound} \\ \text{Cost ( C) }=8.64\text{ }*\text{ \$1.05} \\ \text{Cost ( C)}=\text{ \$9.07} \end{gathered}`

The cost of part C = $9.07

Step 7 :Let calculate the pounds (W) For machine part D

Given data

`\begin{gathered} \text{Number of inches needed=9.5} \\ \text{Number of pounds per inch= 0.32} \\ \text{Cost per pound= \$2.15} \end{gathered}`
`\begin{gathered} 1\text{ inch= 0.32 pounds} \\ 9.5\text{ inches = 9.5}*\text{ 0.32 pound} \\ 9.5\text{ inches=3.04 pounds} \end{gathered}`

The pounds ( W) for machine part D = 3.04 Pounds

Step 8: Let calculate the COST (C) For machine part D

`\begin{gathered} \text{Cost ( C) = number of pounds }*\cos t\text{ per pound} \\ \text{Cost ( }C)=\text{ 3.04}*\text{ \$2.15} \\ \text{Cost ( }C)=\text{ \$6.54} \end{gathered}`

The cost of part D = $6.54

The total cost will be

`\begin{gathered} \cos t\text{ A + cost B +cost C + cost D} \\ 16.57+20.63+$9.07$+6.54 \\ =\text{ \$52.81} \end{gathered}`

The total cost C = $52.81