Please help Trucks amrive at the loading dock of a wholesale

Please help

Trucks amrive at the loading dock of a wholesale grocer at the rate of 12 per hour A single arew consisting of two workers can load s truck in about 30 minutes. Crew members receive 310 per hour in wages and fringe benefits, and trucks and drivers reflect an hourly oost of $82 The manager is thinking of adding another member to the crew The servioe rste would then be 24 truoks per hour Assume rates are Poisson a. W the third crew member be econonwar? (Round your intermediate and r to 2 decimal places. Omit the \"S\" sign in your response) gbecause, the total cost is sl Yes b. Would s fourth member be justifiable if the resulting service capacity were 28 trucks per hour? (Round your intermediate and final answer to 2 decimal places Omit the \"$\" sign in your response ) No because the total cost is

Solution

Answer:

Given in the question:

= 1.2/hour.

Calculation:

Crew = 2:

µ= 2/hour implying Ls=2/(µ*(µ-)) + (/µ) = 1.5 trucks.

Therefore, total cost = 2*$10 + 1.5*$62 = $113/hour

If we add 3rd Crew:

µ= 2.4/hour, implying Ls=2/(µ*(µ-)) + (/µ) = 1 truck.

Therefore, total cost = 3*$10 + 1*$62 = $92/hour.

If we add 4th Crew:

µ= 2.6/hour, implying Ls=2/(µ*(µ-)) + (/µ) = 0.8571 person.

Therefore, total cost = 4*$10 + 0.8571*$62 = $93.14/hour.

Conclusion:

With respect to the above calculations it can be concluded that addition of 3rd crew will be economical ($92/hour) as compared addition of 4th Crew ($93.14/hour). Therefore Use crew of size 3.