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Answer :
a. If J & B throws out all unsold calendars at the end of July, they should order 698 calendars.
b. If J & B reduces the calendar price to $1 at the end of July and can sell all surplus calendars at this price, they should order 499 calendars.
a. To determine how many calendars should be ordered if J & B throws out all unsold calendars at the end of July, we need to find the order quantity that maximizes profit.
Let's calculate the expected demand for the September-to-July period. The mean demand is given as 500 calendars with a standard deviation of 120.
Since the demand follows a normal distribution, we can use the normal distribution formula to find the probability of demand falling within a certain range. We want to find the probability that demand is less than or equal to a certain value.
Using the z-score formula,
z = (x - μ) / σ
where x is the desired value, μ is the mean, and σ is the standard deviation, we can find the z-score for the desired probability.
Since we want to find the probability of demand being less than or equal to a certain value, we need to find the cumulative probability from the z-score.
Using a z-table or a calculator, we find the z-score for a cumulative probability of 0.8 (representing the demand that can be met with certainty) is approximately 0.84.
Next, we need to calculate the safety stock, which is the buffer inventory to ensure we meet demand without stockouts. The safety stock is equal to the desired service level multiplied by the standard deviation.
Let's assume a desired service level of 95%, which corresponds to a z-score of approximately 1.65.
The safety stock is therefore 1.65 * 120 = 198.
To calculate the order quantity, we need to add the safety stock to the mean demand:
Order quantity = mean demand + safety stock
= 500 + 198
= 698.
Therefore, if J & B throws out all unsold calendars at the end of July, they should order 698 calendars.
b. If J & B reduces the calendar price to $1 at the end of July and can sell all surplus calendars at this price, the salvage value needs to be taken into account when determining the order quantity.
In this case, the salvage value is $1 per calendar.
To calculate the order quantity, we can subtract the expected demand from the salvage value from the expected demand for the September-to-July period.
Expected demand for the September-to-July period = 500.
Expected demand for the surplus calendars = expected demand - salvage value
= 500 - 1
= 499.
Therefore, if J & B reduces the calendar price to $1 at the end of July and can sell all surplus calendars at this price, they should order 499 calendars.
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