Question

A toy manufacturer uses 52,360 rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 900 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1.50 per wheel per year. Setup cost for a production run is $41. The firm operates 238 days per year. Determine the following:

a. Optimal run size (Round your answer to a whole number, following normal rules of rounding.)
b. Use your final answer from part a to determine minimum total annual cost for carrying and setup. (Round your answer to a whole number.)


c. Cycle time for the optimal run size (Round your answer to two decimal points.)


d. Run time (Round your answer to two decimal points.)

Answer 1

The optimal run size for the rubber wheels is 1692 units, the minimum total annual cost is approximately $41,001, the cycle time is about 1.88 days, and the run time is also about 1.88 days. These values are calculated using the Economic Order Quantity model.

Step-by-step explanation:

The toy manufacturer's problem of determining the optimal production run size can be solved using the Economic Order Quantity (EOQ) model. This model helps to minimize the total carrying costs and setup costs associated with the production of rubber wheels. Let's calculate the optimal run size, total annual cost, cycle time, and run time for the rubber wheels.

To find the optimal run size, we use the EOQ formula:
EOQ = √((2 * Demand * Setup Cost) / Carrying Cost)
Plugging in the given values we get:
EOQ = √((2 * 52,360 * 41) / 1.50) = √((4,293,640) / 1.50) = √(2,862,426.67) = approximately 1692 wheels (rounded to the nearest whole number).

To find the minimum total annual cost, we need to calculate the carrying cost and setup cost using the EOQ (optimal run size). Carrying cost is half the optimal run size times the carrying cost per unit, setup cost is the annual demand divided by the optimal run size times the setup cost. Therefore:
Total Annual Cost = (EOQ/2) * Carrying Cost per unit + (Demand/EOQ) * Setup Cost
Total Annual Cost = (1692/2) * 1.50 + (52,360/1692) * 41 = approximately $41,001 (rounded to the nearest whole number).

Cycle time is the time between two successive production runs and is given by:
Cycle Time = EOQ / Daily Production Rate
Cycle Time = 1692 / 900 = approximately 1.88 days (rounded to two decimal points).

Run time is the time it takes to produce the EOQ and can be found by:
Run Time = EOQ / Daily Production Rate
Run Time = 1692 / 900 = approximately 1.88 days (rounded to two decimal points, which coincidentally is the same as the cycle time in this case due to the constant rate of production).