Final answer:
The producer's supply at the price of $2 is determined by the supply equation. Given the scenario with LED lights, LPS would need to use inventory management strategies to decide the order quantity and potential profits.
Step-by-step explanation:
When considering how much to supply at a price of $2 each, we look at the supply equation provided by the producer. While the original question does not include the specific supply equation, to proceed, we would insert the price of $2 into the supply equation given by the producer's supply curve. This calculation would yield the quantity the producer is willing to supply at that price point. Decisions on production quantities are influenced by factors such as marginal costs, fixed costs, variable costs, and the anticipated revenue.
In the given scenario, the producer sells LED lights to LPS at a cost of $12 each and has a marginal production cost of $1 per item. LPS, in turn, sells the lights at $24 each and expects demand to follow a normal distribution pattern. Any unsold lights are discounted to $3 after two months. To accurately determine optimal order quantity and expected profits, LPS would need to apply inventory management and profit optimization strategies such as calculating the economic order quantity and utilizing a newsvendor model for demand forecasting.