Prest Metal Products manufactures and sells various products. The products are manufactured at one of a few plants $($depending on the product$)$ and then shipped to a distribution center for eventual delivery to customers. The Auburn Distribution Center $($ADC$)$ of Prest Metal Products handles a subset of Prest Products. The products handled by the ADC are fairly similar in size and weight and differ primarily in features that do not affect handling or packaging.

When the sales staff at Prest receives an order, they send it to the appropriate distribution center to fill $($collect units and package for shipping$)$ and ship the units to the customer. A single order may consist of one $($although unusual$)$ or more units. Regardless of the number of units in the order, ADC has to follow certain steps to process the order, such as verifying the customer's address and credit information, review the order for errors, and so on$.$ The ADC is also responsible for following up on any complaints from the customer about problems with the order.

The ADC expects to distribute $250,000$ units of products next month. As a part of the normal planning process at ADC, the center controller has classified next month's expected operating costs $($excluding costs of the distributed product$)$ as fixed or variable $($with respect to units shipped$)$ as follows.

Account Operating Costs Behavior

Administration $$38,000$ $$36,000$ Fixed

Center labor $$313,000\mathrm{.}00$ $$145,500$ Fixed

Center lease $$129,000\mathrm{.}00$ $$104,000$ Fixed

Depreciation on equipment $$126,200\mathrm{.}00$ $$116,000$ Fixed

Miscellaneous $$128,600\mathrm{.}00$ $$58,000$ Fixed

Order processing $$180,000\mathrm{.}00$ $$42,000$ Fixed

Supervision $$77,500\mathrm{.}00$ $$54,000$ Fixed

Supplies $($including packing materials$)$ $$202,500\mathrm{.}00$ All Variable

Utilites $$87,200\mathrm{.}00$ $$64,000$ Fixed

Total $$1,282,000$

The center manager has asked the financial staff for more information about center costs and whether there is a better way to estimate them rather than having the controller go through the monthly account analysis. The center manager assigned the controller's staff to recommend improvements to the current process.

Historically, all the financial and operation performance measures at ADC have been based on the number of units shipped. However, in preparing the analysis, one of the analysts on the controller's staff collected information from the last twelve months on orders processed as well as units shipped and ADC operating costs. These follow here:

$$1\mathrm{.}00$ $$242,970\mathrm{.}00$ $$10,990\mathrm{.}00$ $$1,000,030$

$$2\mathrm{.}00$ $$248,450\mathrm{.}00$ $$16,500\mathrm{.}00$ $$1,225,470\mathrm{.}00$

$$3\mathrm{.}00$ $$245,750\mathrm{.}00$ $$13,230\mathrm{.}00$ $$1,065,400\mathrm{.}00$

$$4\mathrm{.}00$ $$260,610\mathrm{.}00$ $$15,410\mathrm{.}00$ $$1,205,840\mathrm{.}00$

$$5\mathrm{.}00$ $$256,560\mathrm{.}00$ $$16,970\mathrm{.}00$ $$1,222,720\mathrm{.}00$

$$6\mathrm{.}00$ $$270,740\mathrm{.}00$ $$13,630\mathrm{.}00$ $$1,222,330\mathrm{.}00$

$$7\mathrm{.}00$ $$251,830\mathrm{.}00$ $$16,230\mathrm{.}00$ $$1,158,060\mathrm{.}00$

$$8\mathrm{.}00$ $$282,220\mathrm{.}00$ $$12,880\mathrm{.}00$ $$1,217,190\mathrm{.}00$

$$9\mathrm{.}00$ $$272,760\mathrm{.}00$ $$8,910\mathrm{.}00$ $$1,137,390\mathrm{.}00$

$$10\mathrm{.}00$ $$288,300\mathrm{.}00$ $$12,290\mathrm{.}00$ $$1,164,750\mathrm{.}00$

$$11\mathrm{.}00$ $$285,600\mathrm{.}00$ $$13,300\mathrm{.}00$ $$1,183,670\mathrm{.}00$

$$12\mathrm{.}00$ $$295,770\mathrm{.}00$ $$11,490\mathrm{.}00$ $$1,216,510\mathrm{.}00$

The controller and other managers at ADC agree that operations and costs last year were representative for the center.

a$-1.$ Based on the controller's analysis of accounts, what is the variable cost per case?

a$-2.$ Assuming that $275,000$ units will be shipped in a future month, prepare an estimate of operating costs.

b$.$ Use the high$$low method based on units shipped and center costs to prepare an estimate of operating costs assuming that $275,000$ units will be shipped in a future month.

c$-1.$ Using Excel, calculate a simple regression of operating costs on units shipped and enter the regression coefficients.

c$-2.$ Compute an estimation of operating costs assuming that $275,000$ units will be shipped in a future month by using the results of a simple regression of operating costs on units shipped.

d$-1.$ Using Excel, calculate a multiple regression of operating costs on units shipped and orders processed, and enter the regression coefficients.

d$-2.$ Compute an estimation of operating costs assuming that $275,000$ units based on $13,000$ orders will be shipped in a future month by using the results of a multiple regression of operating costs on units shipped and orders processed.

e$.$ Select the most appropriate estimate for the given circumstances