Question

A museum of natural history opened a gift shop which operates 52 weeks per year. Top-selling item is a bird feeder. Sales are 18 units per week, the supplier charges $60 per unit. Ordering cost is $45. Annual holding cost is 25 percent of a feeder's purchasing cost. Use this information to answer Questions 10-15. Note: Use "1 year = 52 weeks" in your conversions: Management chooses an order quantity of 360 (per order). What is the annual total cost of this policy? Round to the nearest dollar. Hint: Total Cost = Annual Purchasing Cost + Annual Ordering Cost + Annual Holding Cost. Question 11 5 pts Management chooses an order quantity of 36 (per order). What is the annual total cost of this policy? Round to the nearest dollar. Hint: Total Cost = Annual Purchasing Cost + Annual Ordering Cost + Annual Holding Cost. Calculate the EOQ for the museum. Round to the nearest integer. Question 13 What is the annual total cost of the EOQ policy? Round to the nearest dollar

Answer 1

The annual total cost for an order quantity of 360 units is approximately $60,030, whereas for an order quantity of 36 units, the total annual cost is about $68,130. The Economic Order Quantity (EOQ) for the museum is determined to be approximately 53 units.

Step-by-step explanation:

To calculate the annual total cost of the museum's gift shop policy, we need to determine the annual purchasing cost, annual ordering cost, and annual holding cost. For an order quantity of 360 units per order:

• Annual Purchasing Cost = annual demand x cost per unit = 18 units/week x 52 weeks/year x $60/unit = $56,160
• Annual Ordering Cost = (annual demand / order quantity) x ordering cost = (18 x 52) / 360 x $45 = $1,170
• Annual Holding Cost = (order quantity / 2) x (holding cost rate x cost per unit) = (360 / 2) x (0.25 x $60) = $2,700

The Total Cost = $56,160 (Annual Purchasing Cost) + $1,170 (Annual Ordering Cost) + $2,700 (Annual Holding Cost) = $60,030.

For an order quantity of 36 units per order:

• Annual Purchasing Cost remains the same at $56,160
• Annual Ordering Cost = (18 x 52) / 36 x $45 = $11,700
• Annual Holding Cost = (36 / 2) x (0.25 x $60) = $270

The Total Cost = $56,160 + $11,700 + $270 = $68,130.

To calculate the Economic Order Quantity (EOQ), we apply the formula: EOQ = √(2 x annual demand x ordering cost) / holding cost per unit. Plugging in the numbers: EOQ = √(2 x 18 x 52 x $45) / (0.25 x $60) = √(2 x 18 x 52 x $45 / $15) = √(2808) ≈ 53 units (rounded to the nearest integer).

Answer 2

For an order quantity of 360 per order, the annual total cost is $61,566. For an order quantity of 36 per order, the annual total cost is $56,765. The Economic Order Quantity (EOQ) is approximately 161, and the annual total cost for the EOQ policy is $56,415.

Step-by-step explanation:

Total Cost = Annual Purchasing Cost + Annual Ordering Cost + Annual Holding Cost

For management's order quantity of 360 per order:

Annual Purchasing Cost = 18 units per week * $60 per unit * 52 weeks = $56,160

Annual Ordering Cost = $45 per order * (52 weeks / 360 per order) = $6.50

Annual Holding Cost = (0.25 * $60) * 360 per order = $5,400

Total Cost = $56,160 + $6.50 + $5,400 = $61,566 (rounding to the nearest dollar)

For management's order quantity of 36 per order:

Annual Purchasing Cost = 18 units per week * $60 per unit * 52 weeks = $56,160

Annual Ordering Cost = $45 per order * (52 weeks / 36 per order) = $65

Annual Holding Cost = (0.25 * $60) * 36 per order = $540

Total Cost = $56,160 + $65 + $540 = $56,765 (rounding to the nearest dollar)

EOQ (Economic Order Quantity) is the order quantity that minimizes the total cost. It is calculated as:

EOQ = sqrt((2 * Annual Demand * Ordering Cost) / Holding Cost)

Annual Demand = 18 units per week * 52 weeks = 936 units

EOQ = sqrt((2 * 936 * $45) / (0.25 * $60)) ≈ 161 (rounding to the nearest integer)

For the EOQ policy:

Annual Purchasing Cost = 18 units per week * $60 per unit * 52 weeks = $56,160

Annual Ordering Cost = $45 per order * (52 weeks / 161 per order) ≈ $14

Annual Holding Cost = (0.25 * $60) * 161 per order ≈ $241 (rounding to the nearest dollar)

Total Cost = $56,160 + $14 + $241 = $56,415 (rounding to the nearest dollar)