Unit2Math
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Unit 2
**a) How many checkouts did the old system provide in a shift?**
1 shift = 8 hours = 480 minutes
Checkout time for the old system = 45 seconds = 0.75 minutes
Number of checkouts per lane in the old system in 1 shift = \( \frac{480 \text{ minutes}}{0.75
\text{ minutes/checkout}} \)
Since there were 2 old cashier lanes, the total number of checkouts the old system provided in a
shift = 2 x \( \frac{480 \text{ minutes}}{0.75 \text{ minutes/checkout}} \)
**b) How many checkouts does the new system provide?**
Checkout time for the new system = 2 minutes
Number of checkouts per lane in the new system in 1 shift = \( \frac{480 \text{ minutes}}{2
\text{ minutes/checkout}} \)
Since there are 4 scanning stations in the new system, the total number of checkouts the new
system provided in a shift = 4 x \( \frac{480 \text{ minutes}}{2 \text{ minutes/checkout}} \)
**c) What is the multifactor productivity for each system?**
Multifactor productivity (MFP) is calculated as:
\[ MFP = \frac{\text{Output}}{\text{Input}} \]
Where:
- Output = Number of checkouts
- Input = Total costs (labor, electricity, bagging, and capital costs)
For the old system:
Output = Number of checkouts from part (a)
Input = Labor cost (2 workers x $10/hour x 8 hours) + Electricity cost ($0.05 x Number of
checkouts) + Bagging cost ($0.10 x Number of checkouts)
For the new system:
Output = Number of checkouts from part (b)
Input = Labor cost (1 worker x $10/hour x 8 hours) + Electricity cost ($0.05 x Number of
checkouts) + Bagging cost ($0.15 x Number of checkouts) + Capital cost ($100)
Now, let's calculate the values for each part.
**a) How many checkouts did the old system provide in a shift?**
Number of checkouts per lane in the old system in 1 shift:
= \( \frac{480 \text{ minutes}}{0.75 \text{ minutes/checkout}} \)
= 640 checkouts/lane
Total number of checkouts the old system provided in a shift:
= 2 x 640
= 1280 checkouts
**b) How many checkouts does the new system provide?**
Number of checkouts per lane in the new system in 1 shift:
= \( \frac{480 \text{ minutes}}{2 \text{ minutes/checkout}} \)
= 240 checkouts/lane
Total number of checkouts the new system provided in a shift:
= 4 x 240
= 960 checkouts
**c) What is the multifactor productivity for each system?**
For the old system:
Output = 1280 checkouts
Input = Labor cost (2 workers x $10/hour x 8 hours) + Electricity cost ($0.05 x 1280) + Bagging
cost ($0.10 x 1280)
= (2 x $10 x 8) + ($0.05 x 1280) + ($0.10 x 1280)
= $160 + $64 + $128
= $352
MFP (Old system) = \( \frac{1280}{352} \)
= 3.64 checkouts/dollar
For the new system:
Output = 960 checkouts
Input = Labor cost (1 worker x $10/hour x 8 hours) + Electricity cost ($0.05 x 960) + Bagging cost
($0.15 x 960) + Capital cost ($100)
= ($10 x 8) + ($0.05 x 960) + ($0.15 x 960) + $100
= $80 + $48 + $144 + $100
= $372
MFP (New system) = \( \frac{960}{372} \)
= 2.58 checkouts/dollar
In summary:
(a) The old system provided 1280 checkouts in a shift.
(b) The new system provides 960 checkouts.
(c) The multifactor productivity for the old system is 3.64 checkouts/dollar and for the new
system, it's 2.58 checkouts/dollar.
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