D$.$ I will answer general questions but will not give specifics.

E$.$ I hope everyone earns a $100!$ Good luck!

A grocery chain is considering the installation of a set of $4$ self$-$checkout lanes. The new self$-$

checkout lane setup will replace $2$ old cashier lanes that were staffed by a cashier and bagger on

each lane per shift. One cashier mans all $4$ self$-$checkouts per shift $($answering questions, checking

for un$-$scanned items, taking coupons, etc$).$ Checkout on the new lanes takes $1\mathrm{.}25$ 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{.}06$ per checkout while bagging $($material$)$ costs

are $$0\mathrm{.}12$ per checkout with the old system and $$0\mathrm{.}20$ for the new system. The new $4$ self$-$checkout

lanes also requires a total of $$25$ in capital costs per day. Assume that the lanes are always in use for

$16$ hours per day $(2$ shift$),$ for the old system the average revenue per checkout is $$12$ and $$10$ for

the new system, and a worker $($cashier and bagger$)$ makes $$\frac{10}{?}$ hour.

a$.$ How many checkouts in total did the old system provide in a shift?

b$.$ How many checkouts in total does the new system provide in a shift?

c$.$ What is the unit$-$less multifactor productivity for each system $($old or new$)?$

d$.$ Which checkout system is more productive and what is the percent change in productivity for the

new system relative to the old system $(($new$-$old$)/$old$*100)?$