I have the answers but I need detailed help with showing how to get those answer
ID: 353828 • Letter: I
Question
I have the answers but I need detailed help with showing how to get those answers. Thank you!
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 driver-truck costs. The manager has learned that each driver-truck combination represents a cost of $250 per day and that each dock plus loading crew represents a cost of S1,138 per day. 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): 1 b. The manager is considering renting 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 crew working at a dock. What is the optimal daily total cost with the new equipment? What is the optimal daily total cost with the current (oniginal) equipment (from your analysis in part a )? (Round your cost amount to 2 decimal places and all other calculations to 4 decimal places. Omit the "S" sign in your response.) The optimal daily total cost with the new equipment would be $ 1822.00, and the optimal dailty total cost with the original equipment is $ 2138Explanation / Answer
a)
Cost of operating dock plus crew, Cs = 1138 per day
Cost of waiting of driver-truck combo, Cw = 250 per day
Arrival rate, = 4 trucks per day
Service rate, = 5 trucks per day
Number of trucks-driver in system, L = /(-) = 4/(5-4) = 4
Total operating cost with 1 dock = Cs*M + Cw*L = 1138*1 + 250*4 = $ 2138 per day
With 2 docks, Cost of operating docks itself will be 2*1138 = 2276 . and total operating cost will be even more.
Therefore daily operating cost is lesser for 1 dock (=$ 2138).
Number of docks = 1
b)
New parameters
Arrival rate, = 4 per day
Service rate, = 5.71 per day
Number of trucks-driver in system, L = /(-) = 4/(5.71-4) = 2.339
Daily operating cost = (1138+100)+250*2.339 = $ 1822.8
The optimal daily total cost with the new equipment would be $ 1822.8 and the optimal daily total cost with the original equipment is $ 2138
Daily operating cost is lesser with the new equipment. Therefore, it is beneficial to rent new equipment.