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kifflom
1 month ago
6

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 1.25 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 $0.06 per checkout while bagging (material) costs are $0.12 per checkout with the old system and $0.20 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 $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?
Business
1 answer:
arsen [2.9K]1 month ago
6 0

Answer:

a. 2560 checkouts

b. 3072 checkouts

c. Old system = 3.85 checkouts per dollar

New system = 5.56 checkouts per dollar

Explanation:

Provided:

Checkout lanes = 4

a.

What was the total number of checkouts provided by the old system during a shift?

Lanes = 2

Operating time = 16 hours --- Convert to seconds

Time = 16 * 3600 = 57600 seconds

Checkout speed = 1 every 45 seconds

The total number of checkouts is determined as follows:

2 lanes * 57600 seconds * 1 checkout / 45 seconds

Total checkouts = 2560 checkouts

b.

How many checkouts does the new system yield?

Lanes = 4

Operating time = 16 hours --- Convert to minutes

Time = 16 * 60 = 960 minutes

The total number of checkouts is calculated as:

4 lanes * 960 minutes * 1 checkout / 1.25 minutes

Total checkouts = 3072 checkouts

c.

Provided

Electricity costs for both systems are $0.06 per checkout

Bagging (materials) costs are $0.12 per checkout with the old system

Bagging (materials) costs are $0.20 per checkout with the new system

The cost for the old system is calculated as:

$0.06 * 2560 + $0.12 * 2560

= $153.6 + $307.2

= $460.3

Multifactor = 2560 checkouts/$460.3

Multifactor = 5.56 checkouts/$

The cost for the new system is calculated as:

0.06 * $3072 + 0.20 * $3072

= $184.32 + $614.4

= $798.72

Multifactor = 3072 checkouts/$798.72

Multifactor = 3.85 checkouts/$

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