Please answer the following question correctly: The manager of a regional wareho
ID: 346756 • Letter: P
Question
Please answer the following question correctly:
The manager of a regional warehouse must decide on the number of loading docks to request for a new facility in order to minimize the sum of dock costs and drivertruck costs. The manager has learned that each driver-truck combination represents a cost of $296 per day and that each dock plus loading crew represents a cost of $1145 per day. Use Table 1 and Table 2. a. How many docks should be requested if trucks arrive at the rate of four per day, each dock can handle five trucks per day, and both rates are Poisson? Number of dock(s) b. An employee has proposed adding new equipment that would speed up the loading rate to 5.71 trucks per day. The equipment would cost an additional $100 per day for each dock. Should the manager invest in the new equipment? (Round your cost amount to 2 decimal places and all other calculations to 3 decimal places. Omit the "$" sign in your response.) (Click to select) , because the daily total cost with the new equipment is $ which is lower than without the new equipment.Explanation / Answer
To be calculated:
(a) Number of dock(s)
(b) To purchase the new equipment or not
Given values:
Cost of each driver-truck combination = $296 per day
Total cost = $1,145 per day
Truck arrival rate = 4 per day
Capacity of 1 dock = 5 trucks per day
Solution:
(a) Required number of docks is calculated as;
Number of trucks arriving each day = 4
Number of trucks each dock can handle = 5
It is clear that the capacity of handling trucks of each dock is more than the number of trucks arriving on a particular day. Hence, only 1 dock should be requested.
Number of dock = 1
(b) New equipment cost = $100 per day per dock
Increased loading rate = 5.71 trucks per day
The current daily total cost per dock is calculated as;
Current daily total cost = Total cost / Number of trucks
Current daily total cost = $1,145 / 4
Current daily total cost = $286.25
After adding the new equipment, the daily total cost per dock is calculated as;
New daily total cost = Total cost / New loading rate
New daily total cost = ($1,145 + $100) / 5.71
New daily total cost = $1,245 / 5.71
New daily total cost = $218.04
The manager should invest in the new equipment because the daily total cost with the new equipment is $218.04 which is lower than without the new equipment.