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 amount of time in-between trips to the cat food store if Geoff wisely elects to follow an EOQ policy for obtaining cat food.

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 amount of time in-between trips to the cat food store if Geoff wisely elects to follow an EOQ policy for obtaining cat food.

BlackTom AI · Accepted Answer

We’re given Scenario 9.9 data and asked to determine the time between EOQ-replenishment trips for cat food.
First, restating the key figures: there are 7 cats, each eats about 1 can per day, so annual demand D = 7 × 1 × 365 = 2,555 cans/year. The price per can is $0.89, and the holding cost is 10% of unit price, so h = 0.10 × $0.89 = $0.089 per can per year. The travel cost per replenishment order comes from gasoline use: the pickup uses 1 gallon each way, so a round trip consumes 2 gallons. At $3.50 per gallon, the travel cost per trip is S = 2 × $3.50 = $7 per order. Using the EOQ formula EOQ = sqrt(2DS / h) with D = 2,555, S = $7, h = $0.089:

Option-wise evaluation:
Option A: about six months
- If the EOQ calculation yields a time between orders around 6 months, that would correspond to an annual number of orders about 2 per year. Given D = 2,555 cans/year and EOQ ≈ 634 cans (see below), the number of orders per year would be 2,555 / 634 ≈ 4.0 orders/year, i.e., roughly every 3 months, not every 6 months. Hence six months is not supported by the data.

Option B: about three months
- Compute EOQ: 2DS = 2 × 2,555 × 7 = 35,770. Divide by h: 35,770 / 0.089 ≈ 402,000. Square root: sqrt(402,000) ≈ 634 cans per order. The order frequency is D / EOQ = 2,555 / 634 ≈ 4.0 orders/year. Time between orders = 1 year / 4 ≈ 0.25 years. 0.25 × 12 months = 3 months. This matches the calculated interval and aligns with the EOQ model using the given costs.

Option C: about three weeks
- Three weeks ≈ 0.067 years. That would require roughly 15 orders per year (0.067 × 12 ≈ 0.8? Actually 0.067 years corresponds to ~18 days; 365/18 ≈ 20 orders/year). The EOQ-based cadence of ≈4 orders/year is far from 20 per year, so three weeks is inconsistent with the EOQ result given these inputs.

Option D: about three days
- Three days is about 0.0082 years and would imply roughly 365/3 ≈ 122 orders per year. This is far more frequent than the EOQ solution computed with the stated demand and costs, so this is clearly incorrect under the EOQ model here.

Synthesis of the options: the EOQ calculation with D = 2,555 cans/year, S = $7 per order, and h = $0.089 per can per year yields EOQ ≈ 634 cans. ThisD / EOQ results in about 4 orders per year, i.e., one every 0.25 years, which is about 3 months. Therefore, the option that states 'about three months' is the correct interval under the EOQ policy. The other options are inconsistent with the derived EOQ quantity and order frequency given the data.

MGS310001.2025FA Test 03: Chap 10,11

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