A Toy Manufacturer Makes Its Own Wind-Up Motors, Which Are

question 6

Essay

A toy manufacturer makes its own wind-up motors, which are then put into its toys. While the toy manufacturing process is continuous, the motors are intermittent flow. Data on the manufacture of the motors appears below.
Annual demand (D) = 50,000 units Daily subassembly production rate = 1,000
Setup cost (S) = $85 per batch Daily subassembly usage rate = 200
Carrying cost = $.20 per unit per year
a. To minimize cost, how large should each batch of subassemblies be?
b. Approximately how many days are required to produce a batch?
c. How long is a complete cycle?
d. What is the average inventory for this problem?
e. What is the total inventory cost (rounded to nearest dollar) of the optimal behavior in this problem?

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Definitions:

Total Surplus

The total societal benefits from trading a good or service, encapsulated by the combination of consumer surplus and producer surplus in a market.

Average Total Cost

The total cost divided by the quantity produced, denoting the cost per unit of production.

Natural Monopoly

A market structure where a single supplier is most efficient in producing the goods due to high fixed or startup costs, making it unfeasible for new entrants to compete.

Producer Surplus

The variance between the intended selling price by producers and the real price they end up receiving.