$10-28.$ ESTIMATING A COST FUNCTION, HIGH$-$LOW

METHOD. Lynsay Detz is examining customer$-$service costs in the southern region of Clancey Products. Clancey Products has more than $200$ separate electrical products that are sold with a $6-$month guarantee of full repair or replacement with a new product. When a product is returned by a customer, a service report is prepared. This service report includes details of the problem and the time and cost of resolving the problem. Weekly data for the most recent $8-$week period are as follows:

$\backslash$begin$\{$tabular$\}\{$ccc$\}$

Week & Customer$-$Service Department Costs & Number of Service Reports $\backslash \backslash$

$\backslash$hline $1$ & $\backslash (\backslash$$ $13,400\backslash )$ & $210\backslash \backslash$

$2$ & $20,200$ & $300\backslash \backslash$

$3$ & $11,300$ & $130\backslash \backslash$

$4$ & $18,900$ & $385\backslash \backslash$

$5$ & $14,700$ & $285\backslash \backslash$

$6$ & $22,500$ & $450\backslash \backslash$

$7$ & $16,300$ & $330\backslash \backslash$

$8$ & $21,600$ & $310$

$\backslash$end$\{$tabular$\}$

Required

$1.$ Plot the relationship between customer$-$service costs and number of service reports. Is the relationship economically plausible?

$2.$ Use the high$-$low method to compute the cost function relating customer$-$service costs to the number of service reports.

$3.$ What variables, in addition to number of service reports, might be cost drivers of weekly customer$-$service costs of Clancey Products?