# Math Help - Challenging problems

1. ## Challenging problems help

Challenging problems,

A company has the following demand forecast for the next year, expressed in six bimonthly (2-month) periods:

Period Forecast Demand (Standard Units of Work)
1 400
2 380
3 470
4 530
5 610
6 500

a) Assume that an employee contributes 176 regular working hours each month and that each unit requires 20 standard hours to produce. How many employees will be needed during the period the peak demand of 610 units in period 5 if no overtime production id to be scheduled?
b) What will be the average labor cost for each unit if the company pays employees $6 per hour and maintains for the entire year a sufficient staff to meet the peak demand without overtime? c) What percentage above the standard-hour cost is the company’s average labor cost per unit in this year due to the company’s decision to maintain stable employment sufficient to serve the peak demand period without overtime? 2. Originally Posted by Samyeo Challenging problems, A company has the following demand forecast for the next year, expressed in six bimonthly (2-month) periods: Period Forecast Demand (Standard Units of Work) 1 400 2 380 3 470 4 530 5 610 6 500 a) Assume that an employee contributes 176 regular working hours each month and that each unit requires 20 standard hours to produce. How many employees will be needed during the period the peak demand of 610 units in period 5 if no overtime production id to be scheduled? each man contributes 176 hours a month, which means 352 hours bimonthly. each of the 610 units of work require 20 hours to do, which means $610 \cdot 20=12,200$. Each employee, as said before, works 352 hours during the period, which means $12,200\div 352 \approx 35$. So 35 workers are needed. Originally Posted by Samyeo b)What will be the average labor cost for each unit if the company pays employees$6 per hour and maintains for the entire year a sufficient staff to meet the peak demand without overtime?
We know 35 workers are needed to maintain peak demand. There are 12 months per year, and they work 176 hours per month, and we want to find the average for every two months, so $\frac{176\cdot35\cdot12\cdot2064}{6}=72240$. Therefore, the company needs to spend an average of \$72,240 per peak period.

Originally Posted by Samyeo
c) What percentage above the standard-hour cost is the company’s average labor cost per unit in this year due to the company’s decision to maintain stable employment sufficient to serve the peak demand period without overtime?
The equation to find this would be "72,240/average amount of money that would have been paid to match the minimum of each peak period". To find the amount of money that would have been paid to match the minimum of each peak period, we will have to add the cost of each peak period. So let's figure out each one....(please note, 2,064 is how much each employee recieves bimonthly)

1) $\left(\frac{400\cdot20}{352}\right)\cdot2064 \approx 23\cdot2064\approx47472$

2) $\left(\frac{380\cdot20}{352}\right)\cdot2064 \approx 22\cdot2064\approx45408$

3) $\left(\frac{470\cdot20}{352}\right)\cdot2064 \approx 27\cdot2064\approx55728$

4) $\left(\frac{530\cdot20}{352}\right)\cdot2064 \approx 31\cdot2064\approx63984$

5) $\left(\frac{610\cdot20}{352}\right)\cdot2064 \approx 35\cdot2064\approx72240$

6) $\left(\frac{500\cdot20}{352}\right)\cdot2064 \approx 29\cdot2064\approx59856$

Now we add them together, which equals 344,688, and divide that by six and the average is 57,448. Now put that into the original equation...

$\frac{72240}{57448}=1.25748503\approx1.26$
so the amount of percentage above the whatever is around 126%