Question

The Domino taxi company uses 200,000 gallons of gasoline per year at a consistent rate. The cost per gallon of gasoline is $1.80. It costs $40 to have the truck come to the garage and deliver gasoline and to process the orders. Evaporation losses and other storage costs are 10% per year.

1. Should the company spend $4460 to have an additional storage tank installed? Why or Why not?
2. What is the penalty if the company can purchase only 7500 gallons at each order due to the tank’s holding capacity?
3. What is the total annual ordering and carrying cost?

The tanks holding capacity is 7500 gallons at each order.

Answer 1

Let us start by analyzing the total ordering and carrying cost at the present arrangement .

Total cost of gasoline - 200,000 gallons * $ 1.8 = $ 360,000

The tank holding capacity is 7500 gallons for each order and the trucking costs are $40 per order

So , number of order deliveries needed is approx 27 . So total trucking cost is $1080 .

Total Ordering Cost is $ 361080.

Storage costs are 10% per year . So carrying cost is $ 36000.

Overall Cost is $ 397,080 .

What is the saving if the company is adding further storage of 75000 gallons

Trucking cost will come down by 50% . Savings $ 540 .

$4460 is the cost of adding capacity .

No of years for recovering sunk cost is 8.25 years .

In these years storage tank will undergo depreciation as well .

So it is not prudent to add capacity .

The penalty or loss or not adding capacity is $540 per year .

Answer 2

1. Should the company spend $4,460 to install an additional storage tank? Why or why not?

Step 1: Calculate the Economic Order Quantity (EOQ)
The EOQ formula is:

$$EOQ=\sqrt{\frac{2DS}{H}}$$

Plugging in the numbers:

$$EOQ=\sqrt{\frac{2\times 200,000\times 40}{0.18}}=\sqrt{\frac{16,000,000}{0.18}}\approx \sqrt{88,888,888.89}\approx 9,428\text{ gallons}$$

Step 2: Compare EOQ with current tank capacity

• The optimal order size (EOQ) is 9,428 gallons, but the current tank can only hold 7,500 gallons.

• This means the company is forced to order smaller quantities more frequently, leading to higher total costs.

Step 3: Calculate total costs with and without the new tank

• Current setup (Q = 7,500 gallons):

• Ordering cost:

• Carrying cost:

• Total cost: $1,066.67+$675 = $1,741.67

• With new tank (Q = EOQ = 9,428 gallons):

• Ordering cost:

• Carrying cost:

• Total cost: $848.40+$848.40 = $1,696.80

Step 4: Compare savings vs. cost of the new tank

• Savings per year: $1,741.67-$1,696.80 = $44.87

• Cost of the new tank: $4,460

 

Answer: No, the company should not spend $4,460 on the additional storage tank because the savings are too small to justify the cost.

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2. What is the penalty if the company can only purchase 7,500 gallons per order?

The "penalty" is the additional cost incurred by not ordering at the EOQ (9,428 gallons).

Step 1: Calculate total cost at EOQ vs. current Q

• Total cost at EOQ (9,428 gallons): $1,696.80

• Total cost at current Q (7,500 gallons): $1,741.67

Step 2: Compute the penalty

$$Penalty=\mathrm{\$}1,741.67-\mathrm{\$}1,696.80=\mathrm{\$}44.87\text{ per year}$$

Answer: The penalty is $44.87 per year due to the smaller order size.

                      

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3. What is the total annual ordering and carrying cost?

From part 1, we already calculated this for the current setup (Q = 7,500 gallons):

• Ordering cost: $1,066.67

• Carrying cost: $675

• Total annual cost: $1,066.67+$675 = $1,741.67

Answer: The total annual ordering and carrying cost is $1,741.67