# MATHEMATICS

6.13 use Pareto analysis to investigate the following data collected on a printed-circuit-board assembly line:

Defect | Number of Defect Occurrences |

Components not adhering | 143 |

Excess adhesive | 71 |

Misplaced transistors | 601 |

Defective board dimension | 146 |

Mounting holes improperly positioned | 12 |

Circuitry problems on final test | 90 |

Wrong component | 212 |

**a) Prepare a graph of the data.**

**b) What conclutions do you reach?.**

uestion 1

The marginal product of labor can be illustrated geometrically as the:

Select one:

A. slope of the total product curve with respect to labor

B. slope of the total product curve with respect to capital

C. slope of a chord from the origin out to the total product curve at the specified level of labor

D. inverse of the slope of a chord from the origin out to the total product curve at the specified level of labor

E. slope of the total product curve with respect to labor divided by the slope of the total product curve with respect to capital

** **

** **

** **

** **

**Question ****2**

In the table below, the marginal product of labor at *L* = 6 is:

Select one:

A. 3

B. 2

C. 5 = Q for 6^{th} L –Q for 5^{th} L = 18-13 = 5

D. 4

E. 1

** **

** **

**Question ****3**

Output is produced according to *Q* = 4*LK*, where *L* is the quantity of labor input and *K* is the quantity of capital input. If the price of *K* is $10 and the price of *L* is $5, then the cost minimizing combination of *K* and *L* capable of producing 32 units of output is:

Select one:

A. *L* = 8 and *K* = 1

B. *L* = 4 and *K* = 2

C. *L* = 2 and *K* = 2

D. *L* = 2 and *K* = 4

E. *L* = 1 and *K* = 8

Q should be 32 so,

LK = 32/4 = 8.

So, there are 4 choices as given in options.

Option 1: Total cost = 8*5+1*10 = $50

Option 2: Total cost = 4*5+2*10 = $40

Option 3: Total cost = 2*5+4*10 = $50

Option 4: Total cost = 1*5+8*10 = $85

Hence the answer.

** **

**Question ****4**

If output is produced according to *Q* = 3*K* + 4*L*, then this production process exhibits:

Select one:

A. increasing returns to scale

B. decreasing returns to scale

C. first increasing and then decreasing returns to scale

D. constant returns to scale

E. first decreasing and then increasing returns to scale

Q(M) = 3(K+M)+4(L+M) = 3K+4L+7M > 3K+4L+M

** **