Brown\'s, a local bakery, is worried about increased costs particularly energy.
ID: 458217 • Letter: B
Question
Brown's, a local bakery, is worried about increased costs particularly energy. Last year's records can provide a fairly good estimate of the parameters for this year. Wende Brown, the owner, does not believe things have changed much, but she did invest an additional $2,500 for modifications to the bakery's ovens to make them more energy efficient. The modifications were supposed to make the ovens at least 20% more efficient. Brown has asked you to check the energy savings of the new ovens and also to look over other measures of the bakery's productivity to see if the modifications were beneficial. You have the following data to work with: Energy productivity increase = 10.69 % (enter your response as a percentage rounded to two decimal places and include a minus sign if necessary). Capital productivity increase = % (enter your response as a percentage rounded to two decimal places and include a minus sign if necessary). Labor productivity increase = % (enter your response as a percentage rounded to two decimal places and include a minus sign if necessary).Explanation / Answer
--
--
Formula:
let p = productivity
let pn = Productivity now
n = now
ly = last year
ply = productivity last year
prod = produced units = 1500
pcp = percentage change in productivity
productivity ly = production ly / labor hours
= 1500/350 = 4.29 dozen bread loafs per hour
productivity now = production n / labor hours
= 1500/325 = 4.62 dozen bread loafs per hour
pcp = ( Productivity now – productivity last year ) / (productivity last year) * 100%
in short form,
pcp = pn-ply/ply*100 =
(4.62 – 4.29 ) / 4.29 * 100 = 7.69
pn=4.62
ply=4.29
pcp = 7.69%
Energy consumption last year = Produced quantity * Dozen (=12) / energy consumption
= 1500 * 12 / 3,000
= 6
Energy consumption now = 1500 * 12 / 2(7+1)00
= 6.429
The difference = 6.429-6=0.429
3000 – 0.429
100 – 0.429*100/3000 = 0.0143
2(7+1)00 – 0.429
100 – 0.429*100/2(7+1)00 = 0.015321429
difference = 0.015321429-0.0143 = 0.001021429
0.015321429-0.014252419= 0.0010690102 = 10.69%
% change = difference/last year * 100
= 0.429/6 * 100
= 7.15%
pcp for capital:
ly: 16000/1500=10.67
n: (17500+1000)/1500=12.33
pcp = pn-ply/ply*100
= (12.33-10.67)/10.67*100
= 15.56%
--
-- The method below is the hardest way –
Hence can be ignored --
The question already gave one answer 10.69% as the energy productivity rise
How this 10.69% came: (we will do backward chaining
or back tracking)
Once we find it, we can apply the same logic for the other 2 % viz. capital and the labor:
10.69 = 21.3(7+1)/2
21.3(7+1) = 320.7 – 299.32
320.7 = 10.69 * 30
299.32 = 10.69 * 2(7+1)
30 = 3000/100
2(7+1) = 2(7+1)00/100
3000 = $3000 = the old energy cost = power bill last year
2(7+1)00 = $2(7+1)00 = the new energy cost = power bill this year (now)
if 10.69 is for 100, then for 3000 how much?
100 – 10.69
3000 – how much
= 10.69*3000/100 = 320.7
--
Similarly,
If if 10.69 is for 100, then for 2(7+1)00 how much?
100 – 10.69
2(7+1)00 – how much
= 10.69*2(7+1)00/100 = 299.32
Hence
Last year: 320.7
Now: 299.32
The difference = 320.7 - 299.32 = 21.3(7+1)
There are 2 years involved, hence dividing 21.3(7+1) by 2
21.3(7+1)/2 = 10.69 = 10.69% already given in the question
So now, we will devise a formula using forward chaining:
Let z = the % rise in energy productivity
But presently let us assume that we do not know the value of z and try to find (we must get z = 10.69%, if so our method is correct)
Let Nr = Numerator
M = Minuend
S = Subtrahend
z = Nr / 2
Where
Nr = M-S
Where
M = z*3000/100
S = z*2(7+1)00/100
Nr = M-S = z*3000/100 - z*2(7+1)00/100 =
Take out z as common,
Nr = z*(3000/100-2(7+1)00/100)
= z * (30-2(7+1))
= z * 2
Nr = 2z
z = Nr/2
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.