Unit $2$ Exercises

Question $2\mathrm{.}1$

Walmart Canada debuted a new checkout system called "fast lane" that lets customers avoid cashiers and registers. Here's how it works: My Walmart users scan items with their phones as they shop. Once a user is finished shopping, they click "checkout" to receive a barcode. Next, the customer scans the order barcode at one of four scanning stations in the fast lane. This action charges the credit card the My Walmart user has on file. Finally, just before exiting the store, customers present their mobile receipts to a worker tending the fast lane. The system has debuted in a newly opened store in Toronto that Walmart says will serve as a prototype for future store renovations. Assume the new fast lane setup will replace $2$ old cashier lanes that were staffed by a cashier and bagger on each lane. One worker mans all $4$ scanning stations $($answering questions, checking for un$-$scanned items, taking coupons, etc$).$ Checkout on the new lanes takes $2$ minutes $($customers bag their own orders$)$ while checkout with the old lanes took only $45$ seconds. In addition, the electricity costs for both setups are $$0\mathrm{.}05$ per checkout while bagging $($material$)$ costs are $$0\mathrm{.}10$ per checkout with the old system and $$0\mathrm{.}15$ for the new system. The new lanes also require $$100/$shift in capital costs. Assume that the lanes are always in use for $8$ hours per day $(1$ shift$)$ and that a worker makes $$\frac{10}{?}$ hour.

$($a$)$ How many checkouts did the old system provide in a shift?

$($b$)$ How many checkouts does the new system provide?

$($c$)$ What is the multifactor productivity for each system?