Answer :
The optimal production schedule is to produce approximately 48 trumpets per week. The number of trumpets ordered in week 6 is 306.
To find the optimal production schedule for the model 85C trumpets, we need to consider the demand and the cost associated with holding inventory.
The demand for the eight-week planning horizon is given as follows: 62, 52, 42, 22, 36, 92, 55, 24.
To calculate the optimal production schedule, we can use the Economic Order Quantity (EOQ) formula. The EOQ formula considers the cost of ordering inventory and the cost of holding inventory.
The cost of ordering inventory (A) is given as $100 per order, and the cost of holding inventory (h) is $1 per unit per week.
The EOQ formula is: EOQ = sqrt((2 * A * D) / h), where D is the total demand for the planning horizon.
First, let's calculate the total demand for the planning horizon by summing up the demand for each week: 62 + 52 + 42 + 22 + 36 + 92 + 55 + 24 = 385.
Next, plug the values into the EOQ formula: EOQ = sqrt((2 * 100 * 385) / 1) = sqrt(77000) ≈ 277.35.
Since the EOQ represents the optimal order quantity, we should round it to the nearest whole number, which gives us 277 trumpets.
Now, let's determine the optimal production schedule. Since the planning horizon is eight weeks, we divide the total demand (385) by the number of weeks: 385 / 8 = 48.125.
This means that, on average, the company should produce approximately 48 trumpets per week to match the demand and minimize inventory costs.
To find the number of trumpets ordered in week 6, we need to sum up the demand for the first six weeks: 62 + 52 + 42 + 22 + 36 + 92 = 306.
Therefore, the number of trumpets ordered in week 6 is 306.
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