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Posted on 2016-07-21

Can you please help me figure this out? Thanks.

Suppose managers at a company wish to meet the increasing demand for color photocopies and to have more reliable service. Based on historical data, the chance that a black-and-white copier will be down for repairs is 0.12. The color copiers are more of a problem and are down 23% of the time. As a goal, they would like to have at least a 99.90% chance of being able to furnish a black-and-white copy or a color copy on demand. They also wish to purchase only four copiers. They have asked for advice regarding the mix of black-and-white and color copiers. Supply them with advice on how to purchase the greatest number of color copiers while also meeting their goal regarding the furnishing of a copy on demand. Provide calculation and reasons to support that advice. (Assume that the color copier can also be used to make a black-and- white copy.)

The manager should purchase

a. 2

b 1

c. 4

d. 0

e. 3

black-and-white copier(s) and

a. 1

b. 0

c. 4

d. 3

e. 2

color copier(s). If they do this, they will have a ____ % chance of being able to furnish at least a black-and-white copy or a color copy on demand.

Suppose managers at a company wish to meet the increasing demand for color photocopies and to have more reliable service. Based on historical data, the chance that a black-and-white copier will be down for repairs is 0.12. The color copiers are more of a problem and are down 23% of the time. As a goal, they would like to have at least a 99.90% chance of being able to furnish a black-and-white copy or a color copy on demand. They also wish to purchase only four copiers. They have asked for advice regarding the mix of black-and-white and color copiers. Supply them with advice on how to purchase the greatest number of color copiers while also meeting their goal regarding the furnishing of a copy on demand. Provide calculation and reasons to support that advice. (Assume that the color copier can also be used to make a black-and- white copy.)

The manager should purchase

a. 2

b 1

c. 4

d. 0

e. 3

black-and-white copier(s) and

a. 1

b. 0

c. 4

d. 3

e. 2

color copier(s). If they do this, they will have a ____ % chance of being able to furnish at least a black-and-white copy or a color copy on demand.

3 Comments

This brings us to quite easy formula:

p_BW^c_BW*p_C^c_C >= 1-0,999

where

p_BW is probability black-and-white is broken

c_BW is count of black-and-white photocopiers

and the same for color (C) photocopiers.

Since BW photocopiers are more reliable and there is no demand for C photocopiers we can simplify the formula to:

p_BW^c_BW >= 0,001

After putting logarithm on both sides we come up with:

c_BW * log(p_BW) <= log(0,001)

c_BW * log(0,12) >= log(0,001)

c_BW >= log(0,001) / log(0,12)

c_BW >=3,26

The solution is to buy 4 BW photocopiers (this is minimal count of photocopiers).

3 BW and 1 C photocopier would meet the criteria as well:

0,12^3*0,23=0,0004<=0,001

2 BW and 2 C photocopier would meet the criteria as well:

0,12^2*0,23^2=0,0008<=0,00

1 BW and 3 C photocopier would not meet the criteria:

0,12^1*0,23^3=0,00146004>0

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