Use Scenario 14.2 to determine the total annual cost of SoxyBack's current system if a series of promotions increases the standard deviation of demand for both the Dandy and Popinjay lines to 10.Assume that the mean weekly demand for both product lines remains the same.

A) $116,672
B) $140,869
C) $128,771
D) $152,967

To calculate the total annual cost of SoxyBack's current system, we need to use the formula:

Total annual cost = Annual ordering cost + Annual holding cost + Annual stockout cost + Annual transportation cost

Annual ordering cost = (Number of orders per year) x (Cost per order)

Let's start by calculating the number of orders per year:

Number of orders per year = (52 weeks per year) / (Replenishment lead time in weeks)

Using UPS, the replenishment lead time is 1 week and orders are placed every 5 weeks, so:

Number of orders per year = 52 / 5 = 10.4

We can round this up to 11, since we can't order a fractional number of times.

Now let's calculate the annual ordering cost for each product:

Annual ordering cost for Dandy = 11 x (350 x 0.75 + 0.33 x 0.2 x 350) = $3,488

Annual ordering cost for Popinjay = 11 x (35 x 0.75 + 0.33 x 0.1 x 35 x 10) = $66

Next, we need to calculate the annual holding cost for each product. We know that the holding cost is 30% of the product cost, and we need to add the cost of safety stock. Since the safety stock provides a CSL of 0.975, we need to calculate the z-score that corresponds to that level of service. Using a standard normal distribution table, we can find that z = 1.96.

Annual holding cost for Dandy = (0.3 x 350) x (0.2 x 3 + 1.96 x 6) = $54.92

Annual holding cost for Popinjay = (0.3 x 35) x (0.1 x 25 + 1.96 x 6) = $11.83

To calculate the annual stockout cost, we need to find the expected number of units that will be backordered during the lead time. Using the formula for the normal distribution, we can find the z-score that corresponds to a CSL of 0.975, and then calculate the expected number of units using the mean demand, the lead time, and the standard deviation of demand:

z-score for CSL of 0.975 = 1.96

Expected number of backordered units for Dandy = (mH x 1 + z x sH) x lead time = (3 x 1 + 1.96 x 6) x 1 = 19.76

Expected number of backordered units for Popinjay = (mL x 1 + z x sL) x lead time = (25 x 1 + 1.96 x 6) x 1 = 55.76

Using the unit cost and the annual holding cost, we can now calculate the annual stockout cost:

Annual stockout cost for Dandy = 19.76 x 350 x 0.3 = $2,305.56

Annual stockout cost for Popinjay = 55.76 x 35 x 0.3 = $586.08

Finally, we need to calculate the annual transportation cost using UPS. We can use the average demand for each product over the lead time and the formula:

Total weight = (Weight per unit) x (Number of units)

Total transportation cost for Dandy = 52 x 0.2 x (3/5) x (0.75 + 0.33 x 0.2 x 350) = $1,879.68

Total transportation cost for Popinjay = 52 x 0.1 x (25/5) x (0.75 + 0.33 x 0.1 x 35 x 10) = $3,148.96

Adding up all the costs, we get:

Total annual cost = $3,488 + $66 + $54.92 + $11.83 + $2,305.56 + $586.08 + $1,879.68 + $3,148.96 = $11,541.71

Therefore, the total annual cost of SoxyBack's current system with a standard deviation of 10 is $11,541.71.

Option A would increase the transportation cost, but might reduce the holding cost and the stockout cost. Option B would reduce the transportation cost and eliminate the need for local inventories, but might increase the holding cost and the stockout cost. To determine the best choice, we would need to calculate the total annual cost for each option and compare them.