A supplier to Toyota stamps out parts using a press. Changing a part type requires the supplier to change the die on the press. This changeover currently takes four hours. The supplier estimates that each hour spent on the changeover costs $250. Demand for parts is 1,000 per month. Each part costs the supplier $100, and the supplier incurs an annual holding cost of 25%.
a. Determine the optimal production batch size for the supplier.
b. Toyota wants the supplier to reduce its batch size by a factor of 2; that is, if the supplier currently produces Q parts per batch, Toyota would like them to produce Q/2 parts per batch. What should the supplier do in order to make this amount optimal for him? (In other words, what setup time creates a scenario in which the optimal batch size drops to 1/2 of its current level?)

The EOQ is 980 units and should reduce the fixed ordering cost to an amount of $62.50.

Explanation:

a) Annual demand=Qty per mth multiply with 12 = 1000 multiply with 12 =12000

Annual demand in USD, A= 12000 multiply with USD 100 (cost of each part) = USD 1200000

Preparation cost, P= 4 hrs changeover time multiply with USD 250 per hr = USD 1000

Annual holding cost, I = 25% = 0.25

EOQ in USD= Root over (2 multiply with A multiply with P divide by I ) = USD 9.79 multiply with 10000 = USD 98000

EOQ in nos. = USD 98000 divide by USD 100 (cos of each part) = 980 units

b)  Q = 980 divide by 4 = 245

In this case, annual carryring cost, C = EOQ 980 by 4 multiply with 0.5 multiply with Unit cost USD 100 multiply with 0.25 = USD 3062.50

Annual demand, D = 1000 per month multiply with 12 = 12000

Ordering cost = C multiply with 245 / D = USD 62.50

answer; /// i believe the correct answer is (all of the above);