Question

A producer sells a certain type of LED lights to LPS, a local hardware store, at $12 each. The marginal production cost for the producer is $1 per item. LPS prices the lights at $23 and expects demand to be normally distributed with a mean of 20,000 and a standard dev of 5,000. LPS places a single order w/ the producer. Currently, LPS discount any unsold lights at the end of two months down to $3, and any lights that did not sell at full price at this price. A plan under discussion is that the producer buys back any number of unsold lights for $8 per item.

a. Under this plan how many items will LPS order?

Answer 1

To determine the number of items LPS will order in the given scenario, we need to find the quantity that maximizes LPS's expected profit. This can be done by calculating the expected profit for different order quantities and choosing the quantity that maximizes the expected profit. The optimal quantity is the one that maximizes expected profit, taking into account both the selling price and the buyback price.

Step-by-step explanation:

The demand for LED lights from LPS, the local hardware store, can be modeled by a normal distribution with a mean of 20,000 and a standard deviation of 5,000. To determine how many items LPS will order under the plan where the producer buys back unsold lights for $8 per item, we need to find the quantity that maximizes LPS's expected profit.

To find this quantity, we can calculate the expected profit for different order quantities and choose the quantity that maximizes the expected profit. The expected profit can be calculated by multiplying the difference between LPS's selling price and the cost to the producer by the probability of selling that quantity, summed over all possible quantities.

Given the demand distribution, the producer's cost, and the buyback price, we can use statistical methods to find the optimal order quantity. The optimal quantity is the one that maximizes expected profit, taking into account both the selling price and the buyback price.