Question

* ** A. A.W.A .A . . Aalbcc 1 Normal Aab AaBbci Aalbcd AaB Aa No Spac... Heading! Heading 2 Te S A contractor has 50 men of the same capacity at work on a job. They can complete the work in 30 days, the working day being 8 hours, but the contract expires in 20 days. He decided to put 20 additional men. If all the men get P300.00 per day for a full or part time a day, and if the liquidated damages are P10000.00 for every full or part day he requires over his contract time, will he complete the work on time, and if not, would he save money by putting enough men to complete it on time?

Answer 1

Total hours required to complete the work = No. of workers * No. of days * Hours worked per day

Total hours required to complete the work = 50 * 30 * 8 = 12000

Regime A (If he doesn't employ additional workers) :

Total hours of work done = 50 * 20 * 8 = 8000

Total days of work remaining = (Total hours required to complete the work - Total hours of work done) / (No. of Workers * Hours worked per day)

Total days of work remaining = (12000-8000)/(50*8) = 10

Total Cost (C_A) = 300*50 + 10*10000 = 15000 + 100000 = 115000

Regime B (If he employs 20 additional workers) :

Total work done = 70 * 20 * 8 = 11200

Total days of work remaining = (Total hours required to complete the work - Total hours of work done) / (No. of Workers * Hours worked per day)

Total days of work remaining = (12000 - 11200)/(70*8) = 1.429 days = 1 full day and 1 part day = 2 full and part days

Total Cost (C_B) = 300*70 + 2*10000 = 41000

Hence, even if he employs 20 additional workers, he'll still wont finish the work on time, but his costs are drastically reduced from 115,000 to 41,000. (C_B < C_A)

If he decides to employ enough men to complete the work in 20 days, then

No of workers required = 12000/(20*8) = 75

Total cost (C_C) = 300*75 = 22500

Since C_C < C_B < C_A ; the contractor would save money by putting enough men to complete the job on time.