Respuesta :
To minimize their total cost, the hospital has to order 100 with a minimum total cost = 1810 because the total annual cost is the lowest when compared to the rest of the cost bracket.
What is called total cost?
Total cost is the sum of all expenses incurred to produce an output of any kind. The total cost of direct materials and labor as well as the total cost of manufacturing overhead can be added together to get the total cost of the product.
Given that:
Annual Demand (D) = 3100
Ordering Cost (S) = 10
Holding Cost (H) = 30
Calculate the economic order quantity (EOQ) and Total annual cost(TAC) to determine which order minimizes the total cost.
Economic order quantity (EOQ)
Formula
EOQ = Sqrt(2× d × S /H)
Total Annual Cost (TAC)
Formula
TAC = (D × S) / EOQ + (EOQ × H) /2 + (D × C)
Now Economic order quantity (EOQ)
EOQ = Sqrt(2 × 3100 × 10/30)
EOQ = Sqrt(2066.66666667)
EOQ = 45.4606056566
EOQ = 45
Total Annual Cost (TAC) of EOQ = 45
TAC = (3100 × 10) / 45 + (45 × 30) / 2 + (3100 × 30)
TAC = 94363.8888889
TAC = 94363.89
Total Annual Cost (TAC) of Q = 100
TAC =(3100 × 10) / 100+ (100 × 3) / 2 + (3100 × 27)
TAC = 85510
Total Annual Cost (TAC) of Q = 500
TAC =(3100 × 10) / 500+ (500 × 3) / 2 + (3100 × 26)
TAC = 88162
Thus it is clearly evident that the hospital has to order 100 with a minimum total cost = 1810 because the TAC is the lowest when compared to the rest of the cost bracket.
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