You need to meet lighting requirement in the specific room You may choose from t

Question

You need to meet lighting requirement in the specific room You may choose from the following two lighting options: Constraints 1. You must have at least 4,000 lumens in total lighting 2. Since area was overwired, you have no wiring or maintenance costs 3. As each light burns out, you must replace with the same light 4. Cost of electricity is $0.11 per kWh and expected to be the same over the next 36 months 5. You only need the room for 36 months. 6. At the end of the period you will not remove lights 7, Lights must be on for 400 hours per month 8. Company MARR = 1% per month Determine best combination of lighting to minimize costs

Explanation / Answer

First lets analyze the data given,

Lumens required for lighting the complete room = 4000 lumens

Cost of electricity = 0.11 $/kWh

No.of hours per month lights must be on = 400 hrs

Total no.of months the room is needed = 36 months

Therefore, Total no.of hours the lights must be on = 36 months * 400 hrs/months = 14400 hrs.

Let us now see the option 1

Option 1 :

Given each light output = 800 lumens

Therefore no.of bulbs required to get the output of 4000 lumens = 4000 lumens / 800 lumens = 5

No.of hours after which lights must be replaced = 300hrs

Therefore total no.of replacements required = 14400 hrs / 300 hrs = 48

So total no.of bulbs required = 48 * 5 = 240 bulbs

Cost per bulb = 18 $

Total cost for purchasing bulbs = 240 * 18 $ = 4320 $

Usage cost of light per bulb = 0.022 kW/hr

As we use 5 bulbs at a time, total usage cost of light = 5 * 0.022 kW/hr = 0.11 kW/hr

So total usage of light for the entire 14400 hours = 0.11 kW/hr * 14400 hrs = 1584 kW

cost of electricity per kW = 0.11 $

Total cost of electricity = 1584 * 0.11 = 174.24 $

The total cost without considering the MARR = Bulbs cost + Electricity cost = 4320 + 174.24 = 4494.24 $

Now lets consider the MARR. MARR is minimun attractive return rate. This is nothing but the amount a project manager receives in order to accept a project. It depends on various factors, which is not required as the MARR % is already given as 1 % per month in this case .

The entire cost over a period of 36months is 4494.24 $ . Therefore cost per month = 4494.24 / 36 = 124.84 $

As the MARR is 1% , its vlue is = 124.84 * (1/100) = 1.2484 $

Lets now caluclate for entire period of 36 months = 1.2484 * 36 = 44.94 $

lets now subtract this from the entire cost to get the total cost with MARR = 4494.24 - 44.94 = 4449.3 $

Total cost for option 1 = 4449.3 $

Let us now see the option 2

Option 2 :

Given each light output = 1100 lumens

Therefore no.of bulbs required to get the output of 4000 lumens = 4000 lumens / 1100 lumens = 3.636 = 4 (rounded of as this must be a integer )

No.of hours after which lights must be replaced = 350hrs

Therefore total no.of replacements required = 14400 hrs / 350 hrs = 41.142 = 42 (as no.of replacements must be integer)

So total no.of bulbs required = 42 * 4 = 168 bulbs

Cost per bulb = 35 $

Total cost for purchasing bulbs = 168 * 35 $ = 5880 $

Usage cost of light per bulb = 0.025 kW/hr

As we use 5 bulbs at a time, total usage cost of light = 4 * 0.025 kW/hr = 0.1 kW/hr

So total usage of light for the entire 14400 hours = 0.1 kW/hr * 14400 hrs = 1440 kW

cost of electricity per kW = 0.11 $

Total cost of electricity = 1440 * 0.11 = 158.4 $

The total cost without considering the MARR = Bulbs cost + Electricity cost = 5880 + 158.4 = 6038.4 $

Now lets consider the MARR.

The entire cost over a period of 36months is 6038.4 $ . Therefore cost per month = 6038.4 / 36 = 167.73 $

As the MARR is 1% , its vlue is = 167.73 * (1/100) = 1.6673 $

Lets now caluclate for entire period of 36 months = 1.6673 * 36 = 60.02 $

lets now subtract this from the entire cost to get the total cost with MARR = 6038.4 - 60.02 = 5978.38 $

Total cost for option 2 = 5978.38 $

Hence the best combination of lighting to minimize costs is OPTION 1

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