Scenario 9.9
"Gollee those cats sure go through a lot of food," Geoff exclaimed as he saw the shopping list pad that had been pre-printed with the words "cat food" at the top. He pondered a different approach to shopping for the furry little darlings, reviewed his shopping records, and discovered the following. The price of cat food has held steady at 89 cents per can. Despite feigning indifference, each of the seven cats nibbles their way through an average of one can per day, three hundred sixty five days a year. The price of gasoline has held constant at $3.50 per gallon and his pickup uses a gallon each way to the cat food store. The cost to hold a can of cat food is 10% of the unit price.

Use the information in Scenario 9.9 to determine the combined cost of goods and inventory if Geoff decides to follow the economic order quantity model?

Question

Scenario 9.9
"Gollee those cats sure go through a lot of food," Geoff exclaimed as he saw the shopping list pad that had been pre-printed with the words "cat food" at the top. He pondered a different approach to shopping for the furry little darlings, reviewed his shopping records, and discovered the following. The price of cat food has held steady at 89 cents per can. Despite feigning indifference, each of the seven cats nibbles their way through an average of one can per day, three hundred sixty five days a year. The price of gasoline has held constant at $3.50 per gallon and his pickup uses a gallon each way to the cat food store. The cost to hold a can of cat food is 10% of the unit price.

Use the information in Scenario 9.9 to determine the combined cost of goods and inventory if Geoff decides to follow the economic order quantity model?

BlackTom AI · Accepted Answer

We start by restating the data and what is being asked. The scenario provides: seven cats averaging 1 can per day for 365 days, so annual demand D = 7 × 365 = 2555 cans. The unit price of cat food is $0.89 per can. The holding cost per unit per year H = 10% of unit price = 0.10 × 0.89 = $0.089 per can per year. The transportation cost to place an order (fuel for round trip) acts as the ordering cost S: round-trip fuel is 2 gallons, gasoline is $3.50 per gallon, so S = 2 × 3.50 = $7.00 per order.

Option by option analysis:

- Option A: $2,218
  This total would need to combine purchasing cost, holding cost, and ordering cost. If we roughly estimate, the annual purchasing cost alone is D × price = 2555 × 0.89 ≈ $2,273.95. Since 2,218 is already lower than the purchasing cost, this option is inconsistent with the basic fact that you must pay at least the purchase cost for the goods. Thus, this option underestimates the minimum possible cost.

- Option B: $2,330
  This is very close to the value we obtain when applying the EOQ formula with the given parameters. Compute EOQ: Q* = sqrt[(2DS)/H] = sqrt[(2 × 2555 × 7) / 0.089] ≈ sqrt[35770 / 0.089] ≈ sqrt[402,000] ≈ 634 cans per order. Annual ordering cost = (D / Q*) × S ≈ (2555 / 634) × 7 ≈ 4.026 × 7 ≈ $28.18. Average inventory = Q*/2 ≈ 317 cans. Annual holding cost = 317 × 0.089 ≈ $28.21. Annual purchasing cost = D × price = 2555 × 0.89 ≈ $2,273.95. Summing: 2,273.95 + 28.18 + 28.21 ≈ $2,330.34, which matches the option when rounded.

- Option C: $2,415
  This value would imply a higher total than the EOQ-calculated total, which would occur if Q* were smaller (increasing ordering costs) or if holding costs or purchasing costs were higher. Given the math above, with the provided parameters the total is around $2,330, not $2,415. The discrepancy indicates this option does not align with the EOQ results under these inputs.

- Option D: $2,274
  This number is very close to the annual purchasing cost alone (approximately $2,273.95). However, the EOQ total also includes ordering and holding costs, which add roughly $56 in this case. So $2,274 would neglect the ongoing costs tied to ordering and inventory, making it an underestimate of the true total cost under EOQ.

To summarize the reasoning in natural terms: the EOQ model balances ordering and holding costs against the fixed annual purchasing cost. The computed EOQ yields an ordering cost around $28 and a holding cost around $28, both added to the purchasing cost of about $2,274, bringing the total to roughly $2,330. The other options either fall short by ignoring part of the costs (like only purchasing) or misprice the balance between ordering and holding relative to D, S, and H.

MGS310001.2025FA Test 03: Chap 10,11

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MGS*3100*01.2025FA Test 03: Chap 10,11