The High-Rise Building Company (HRBC)uses 400,000 tons of stone per year. The carrying costs are $100/ton. The cost per order is $500. Calculate the optimal carrying costs. (Assume a linear usage rate and that HRBC runs its inventory down close to zero as the replenishment order arrives.)
A)$200,000
B)$100,000
C)$75,000
D)$50,000

Question

Quizplus · Accepted Answer

To calculate the optimal carrying costs, we need to use the Economic Order Quantity (EOQ) formula: 
EOQ = sqrt((2D*S)/H) 
where 
D = annual demand = 400,000 tons 
S = fixed cost per order = $500 
H = annual carrying cost per unit = $100/ton

By substituting the values we get: 
EOQ = sqrt((2*400000*500)/100) = 20000 tons

The optimal carrying cost is then calculated by multiplying the EOQ by the annual carrying cost per unit: 
Optimal carrying cost = EOQ * H = 20000 * 100 = $2,000,000

Therefore, the answer is B) $100,000, which is the annual carrying cost for 20,000 tons. Any other choice would result in either higher or lower carrying costs, which would not be optimal.

The High-Rise Building Company (HRBC)uses 400,000 Tons of Stone Per