Tower Distributors provides logistical services to local manufacturers. Tower picks up products from the manufacturers, takes them to its distribution center, and then assembles shipments to retailers in the region. Tower needs to build a new distribution center; consequently, it needs to make a decision on how many trucks to use. The monthly amortized capital cost of ownership is $2,100 per truck. Operating variable costs are $1 per mile for each truck owned by Tower. If capacity is exceeded in any month, Tower can rent trucks at $2 per mile. Each truck Tower owns can be used 10,000 miles per month. The requirements for the trucks, however, are uncertain. Managers have estimated the following probabilities for several possible demand levels and corresponding fleet sizes.Requirements (miles/month) 100,000 150,000 200,000 250,000Fleet Size (trucks) 10 15 20 25Probability 0.2 0.3 0.4 0.1Notice that the sum of the probabilities must equal 1.0. If Tower Distributors wants to minimize the expected cost of operations, how many trucks should it use?
Tower Distributors provides logistical services to local manufacturers. Tower picks up products from the manufacturers, takes them to its distribution center, and then assembles shipments to retailers in the region. Tower needs to build a new distribution center; consequently, it needs to make a decision on how many trucks to use. The monthly amortized capital cost of ownership is $2,100 per truck. Operating variable costs are $1 per mile for each truck owned by Tower. If capacity is exceeded in any month, Tower can rent trucks at $2 per mile. Each truck Tower owns can be used 10,000 miles per month. The requirements for the trucks, however, are uncertain. Managers have estimated the following probabilities for several possible demand levels and corresponding fleet sizes.
Requirements (miles/month) 100,000 150,000 200,000 250,000
Fleet Size (trucks) 10 15 20 25
Probability 0.2 0.3 0.4 0.1
Notice that the sum of the probabilities must equal 1.0. If Tower Distributors wants to minimize the expected cost of operations, how many trucks should it use?
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