  I need a detailed assistance to solve the following problem in: Operations Analysis.1) A trucking company maintains an inventory of trucks that varies monthly.  The ending inventory of trucks during the first 8 months of the year (January to August) were 26, 38, 31, 22, 13, 9, 16, 5, respectively.  The monthly inventory holding cost is proportional to the monthly ending inventory.  Trucks incur the following costsEach truck costs the company \$8,000. Interest rate on the cost of capital is 20% per annum (annually).Each truck incurs a storage cost of 3% per annum of the truck cost.Each truck incurs a liability insurance cost of 2% per annum of the truck cost. The carrying cost is the total of all costs (capital, storage and insurance.)What is the monthly carrying cost per truck?What is the total carrying cost incurred by the company over the 8 months (January to August)? What is the estimated average annual carrying cost?

Question

I need a detailed assistance to solve the following problem in: Operations Analysis.

1) A trucking company maintains an inventory of trucks that varies monthly.  The ending inventory of trucks during the first 8 months of the year (January to August) were 26, 38, 31, 22, 13, 9, 16, 5, respectively.  The monthly inventory holding cost is proportional to the monthly ending inventoryTrucks incur the following costs

• Each truck costs the company \$8,000.
• Interest rate on the cost of capital is 20% per annum (annually).
• Each truck incurs a storage cost of 3% per annum of the truck cost.
• Each truck incurs a liability insurance cost of 2% per annum of the truck cost. The carrying cost is the total of all costs (capital, storage and insurance.)
• What is the monthly carrying cost per truck?
• What is the total carrying cost incurred by the company over the 8 months (January to August)?

• What is the estimated average annual carrying cost?

Step 1

Step1: Calculating the value of monthly carrying cost per truck. We have,

Monthly carrying cost per truck = Capital cost per month + Storage cost per month + Insurance cost per month

Here,

Capital cost per month = (Cost of Truck x Interest rate per annum) / 12

Capital cost per month = (\$8,000 x 20%) / 12 =\$ 133.33

Storage cost per month = Cost of Truck x Storage cost per annum

Storage cost per month = (\$ 8,000 x 3%) / 12 = \$ 20.00

Insurance cost per month = Cost of Truck x Insurance cost per annum

Insurance cost per month = (\$ 8,000 x 2%) / 12 = \$ 13.33

By substituting this value in the above formula. We have,

Monthly carrying cost per truck = \$ 133.33 + \$ 20.00 + \$ 13.33

Monthly carrying cost per truck = \$ 166.67

Step 2

Step2: Calculating the value of the total carrying cost incurred by the company over the 8 months (January to August). We have,

Total ending inventory over the 8 months = 26+38+31+22+13+9+16+5 = 160

The total carrying cost incurred by the company over the 8 months = To...

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