Willard offers infestation services for friendly tenants according to the following price schedule: for up to 99 mice, the price is $1.05 each, for 100 up to 499 mice the price is $1.00 each, and for any order exceeding 500 mice, the cost is $0.95. He has a flat $250 delivery fee regardless of order quantity. Crystal will need 10,000 mice this year and face a $1 holding cost. What is her optimal order quantity?

Question

Quizplus · Accepted Answer

Crystal needs to order enough mice to cover her entire year's demand while minimizing holding costs. Using the Economic Order Quantity formula, we can calculate the optimal order quantity as:

EOQ = sqrt((2DS)/H)

where:
D = annual demand = 10,000 mice
S = setup cost = $250 delivery fee
H = holding cost = $1 per mouse per year

Plugging in the values and solving for EOQ:

EOQ = sqrt((2*10,000*$250)/$1) = 2,236.07

Round up to the nearest integer to get an order quantity of 2,237 mice.

Since Crystal's order exceeds 500 mice, she will pay the lowest price of $0.95 per mouse. Therefore, her total cost will be:

Total Cost = (Number of Mice)*(Price per Mouse) + Holding Cost
Total Cost = (2,237)($0.95) + ($1)(10,000)
Total Cost = $2,263.15

Therefore, the best choice for Crystal is to order 2,237 mice.

Willard Offers Infestation Services for Friendly Tenants According to the Following