# 7.2: An Engineering Cost Analysis Example

**At Grade**Created by: CK-12

Suppose you are a design engineer for a company that manufactures consumer electronic devices and you are estimating the cost of producing a new product. The product has four components that are purchased from electronic parts suppliers and assembled in your factory. You have received cost information from your suppliers for each of the parts; as is typical in the electronics industry, the cost of a part depends on the number of parts you order from the supplier.

Your assembly cost for each unit include the cost of labor and your assembly plant. You have estimated that these costs are

C0=$45.00/unit.

The cost of each part depends on the number of parts purchased; we will use the variable \begin{align*}n\end{align*} to represent the number of parts, and the variables

CA

,

CB

,

CC

,

and

CD

to represent the unit cost of each type of part. These cost are given in Tables 3-6.

n |
CA |
---|---|

\begin{align*}1-4\end{align*} | $\begin{align*}16.00\end{align*} |

\begin{align*}5-24\end{align*} | $\begin{align*}14.00\end{align*} |

\begin{align*}25-99\end{align*} | $\begin{align*}12.70\end{align*} |

\begin{align*}100 \;\mathrm{or\ more}\end{align*} | $\begin{align*}11.00\end{align*} |

n |
CB |
---|---|

\begin{align*}1-9\end{align*} | $\begin{align*}24.64\end{align*} |

\begin{align*}10-49\end{align*} | \begin{align*}24.32\end{align*} |

\begin{align*}50-99\end{align*} | $\begin{align*}24.07\end{align*} |

\begin{align*}100 \;\mathrm{or\ more}\end{align*} | $\begin{align*}23.33\end{align*} |

n |
CC |
---|---|

\begin{align*}1-24\end{align*} | $\begin{align*}17.98\end{align*} |

\begin{align*}25-49\end{align*} | $\begin{align*}16.78\end{align*} |

\begin{align*}50 \;\mathrm{or\ more}\end{align*} | $\begin{align*}15.78\end{align*} |

n |
CD |
---|---|

\begin{align*}1-9\end{align*} | $\begin{align*}12.50\end{align*} |

\begin{align*}10-99\end{align*} | $\begin{align*}10.42\end{align*} |

\begin{align*}100 \;\mathrm{or\ more}\end{align*} | $\begin{align*}9.62\end{align*} |

The unit cost is

Cunit = C0 + CA + CB + CC + CD

.

To find the unit cost to build one unit, we look in the above tables with a value of

n

= 1; the unit cost is

$\begin{align*}45.00 +\end{align*} $\begin{align*}16.00 +\end{align*} $\begin{align*}24.64 +\end{align*} $\begin{align*}17.98 +\end{align*} $\begin{align*}12.50 =\end{align*} $\begin{align*}116.12\end{align*}

To find the unit cost to build \begin{align*}20\end{align*} units, we look in the above tables with a value of

n

= 20 and get

$\begin{align*}45.00 +\end{align*} $\begin{align*}14.00 +\end{align*} $\begin{align*}24.32 +\end{align*} $\begin{align*}17.98 +\end{align*} $\begin{align*}10.42 =\end{align*} $\begin{align*}109.72\end{align*}

As expected, the unit cost for \begin{align*}20\end{align*} units is lower than the unit cost for one unit.

**Exercise 13**

Create an if statement that will assign the proper cost to the variable

CA

based on the value of the variable

n

.

**Exercise 14**

Create a script that will compute the total unit cost

Cunit

for a given value of the variable

n

.

**Exercise 15**

Create a m-file script that will compute and plot the total unit cost

Cunit

as a function of

n

for values of

n

from \begin{align*}1\end{align*} to \begin{align*}150\end{align*}.

**Exercise 16**

Suppose that you decide to fire your workers, close down your plant, and have the assembly done offshore; in this arrangement,

C0 = Cx + Cs

,

where

Cx

is the cost of offshore assembly and

Cs

is the cost of shipping assembled units from the assembler to your warehouse. After some investigation, you find an offshore assembler that gives you the assembly costs as a function of the number of units to assemble shown in Table 7.

n |
Cx |
---|---|

\begin{align*}1-29\end{align*} | $\begin{align*}40.00\end{align*} |

\begin{align*}30-59\end{align*} | $\begin{align*}30.00\end{align*} |

\begin{align*}60 \;\mathrm{or\ more}\end{align*} | $\begin{align*}22.00\end{align*} |

You also find a shipping company that will ship the units from the assembler to your warehouse and whose freight charges are a function of the number of units shipped as shown in Table 8.

n |
Cs |
---|---|

\begin{align*}1-9\end{align*} | $\begin{align*}20.00\end{align*} |

\begin{align*}10-24\end{align*} | $\begin{align*}18.00\end{align*} |

\begin{align*}25-74\end{align*} | $\begin{align*}16.00\end{align*} |

\begin{align*}75 \;\mathrm{or\ more}\end{align*} | $\begin{align*}15.00\end{align*} |

Update the m-file script in Exercise 15 to account for the changes in cost due to offshoring.

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