Case 1: Higgins River Kayaking, Inc.

During the planning session for the next kayaking season, the owner, Maiko Johnson asked you, the Chief Financial Officer for Higgins River Kayaking, Inc., to predict her fuel costs each coming week.

Maiko typically staffs the desk at the river answering the phone, checking in customers, and taking payment while her staff drives the customers and kayaks out to the drop-off point on the river. Since she is not actively driving the van, it has been her process to maintain a separate bank account specifically for fuel costs and giving the debit card tied to the account to her staff. That way, staff members can easily fill the tank on the way back from dropping off customers. Maiko wants to keep a low balance in this account, just sufficient to pay fuel costs for the upcoming week. To that end, she currently checks the balance in the account each Monday morning, and transfers in just enough funds to bring the balance to $330.

Maiko developed this current system as a way of limiting her risk of fraud. Several years ago, Maiko simply gave her credit card to staff members to pay for fuel. One time, a staff member charged an additional $500 (buying gift cards for personal use). The staff member collected their paycheck at the end of the week and was never seen again. When the credit card statement came later that month, Maiko was stuck with the bill. Maiko wants to keep the account balance low to minimize her risk of fraud. At the same time, there is also a risk to keeping that account balance too low. This past season, Maiko had some cash flow issues there were a couple of occasions where the company debit card was declined for insufficient funds at the gas station. This can also be a serious problem. If the card is declined and the van runs out of gas, she may lose customers or get unfavorable Yelp ratings. If the charge does go through when the account has an insufficient balance, Maiko would be liable for overdraft fees. Therefore, Maiko wants to improve from her current process of refilling that account to $330 at the beginning of each week while minimizing both these risks.

Maiko started out by collecting data on each Monday morning, she recorded the price of gas and the number of reservations for the coming week (see the attached Excel spreadsheet). She would like to use one of these measures to estimate the weeks fuel costs, but she is not sure which one would give her the best estimate. The number of reservations tells her how many customers have reserved kayaks for the coming week, but some reservations are later cancelled (or no-shows) and many customers show up unannounced for a trip down the river. In addition, the price of gas on Monday morning usually does not stay the same through the entire week. Maiko knows that neither of these variables will perfectly predict her fuel costs, but figures that anything would be better than her current process.

3. Using least squares regression, develop a cost estimating equation for fuel costs at Higgins River Kayaking. Identify the fixed and variable cost components of your cost estimating equation, and explain what they mean.

B C D E F Week D A 5 6 7 # of reservations Gas price Fuel cost 1 3 $2.55 $153.52 2 20 $2.67 $170.79 3 23 $2.64 $249.39 4 10 $2.43 $204.00 5 15 $2.34 $218.31 6 8 $2.64 $170.17 7 24 $2.58 $212.86 8 13 $2.64 $223.35 9 10 $2.33 $160.63 10 1 $2.26 $139.91 11 29 $2.29 $208.70 12 12 $2.75 $244.41 13 41 $2.67 $287.18 14 17 $2.30 $249.00 15 5 $2.31 $198.09 16 12 $2.33 $250.39 17 42 $2.35 $225.19 18 6 $2.12 $286.29 19 35 $2.87 $274.92 20 19 $2.70 $186.55 21 27 $2.58 $211.33 22 13 $2.72 $246.94 23 19 $2.23 $188.97 24 11 $2.25 $177.65 25 13 $2.55 $149.27 26 9 $2.41 $177.60 8 19 20 21 22 23 24 25 26 27 28 29 30 31 32