Aggregate Planning
Planning Horizon
Aggregate planning: Intermediate-range capacity
planning, usually covering 6 to 18 months.
Long range
Short
range
Now
Intermediate
range
6 months
18 months
3
©The McGraw-Hill Companies, Inc., 2004
Process planning
Long
range
Strategic capacity planning
Intermediate Forecasting
& demand
range
management
Sales and operations (aggregate) planning
Sales plan
Aggregate operations plan
Manufacturing
Services
Master scheduling
Material requirements planning
Short
range
Order scheduling
Weekly workforce and
customer scheduling
Daily workforce and customer scheduling
Operations Planning Activities
• Long-range planning
–
–
Greater than one year planning horizon
Usually performed in annual increments
• Medium-range planning
–
–
Six to eighteen months
Usually with monthly or quarterly increments
• Short-range planning
–
–
One day to less than six months
Usually with weekly increments
Planning Tasks and Responsibilities
Aggregate Production Planning
(APP)
 Matches market demand to company resources
 Plans production 6 months to 18 months in
advance
 Expresses demand, resources, and capacity in
general terms
 Develops a strategy for economically meeting
demand
 Establishes a company-wide game plan for
allocating resources
Balancing Aggregate Demand
and Aggregate Production Capacity
10000
Suppose the figure to
the right represents
forecast demand in
units
Now suppose this
lower figure represents
the aggregate capacity
of the company to
meet demand
10000
8000
8000
6000
7000
6000
5500
4500
4000
2000
0
Jan
Feb
9000
9000
Jan
Feb
Mar
Apr
9900
10000
May
Jun
9500
9500
May
Jun
8800
8000
What we want to do is
balance out the
production rate,
workforce levels, and
inventory to make
these figures match up
6000
4000
2000
0
Mar
Apr
Aggregate Plan: Relationships
Marketplace
and Demand
Demand
Forecasts,
orders
Product
Decisions
Process
Planning & Capacity
Decisions
Aggregate
Plan for
Production
Master
Production
Schedule, and MRP systems
Detailed Work
Schedules
Research and
Technology
Work Force
Raw Materials
Available
Inventory On
Hand
External
Capacity
Subcontractors
Inputs and Outputs to APP
Capacity
Constraints
Demand
Forecasts
Size of
Workforce
Strategic
Objectives
Aggregate
Production
Planning
Production
per month
(in units or $)
Inventory
Levels
Company
Policies
Financial
Constraints
Units or dollars
subcontracted,
backordered, or lost
Aggregate Planning Inputs
Resources
• Workforce
• Facilities
Demand forecast
Policies
•
•
•
•
Subcontracting
Overtime
Inventory levels
Back orders
Common unit for
measuring outputs
Costs
•
•
•
•
•
•
Inventory carrying
Back orders
Hiring/firing
Overtime
Inventory changes
Subcontracting
Aggregate Planning Outputs
• A plan that specifies the optimal combination of
– production rate (units completed per unit of
time)
– workforce level (number of workers)
– inventory on hand (inventory carried from
previous period
– Subcontracting levels (if any)
– Backordering levels (if any)
Aggregate Planning Goals
•
•
•
•
Meet demand
Use capacity efficiently
Meet inventory policy
Minimize total cost
Aggregate Planning Strategies
• Proactive
– Alter demand to match capacity
• Reactive
– Alter capacity to match demand
• Mixed
– Some of each
Demand Management
 Shifting demand into other periods by
incentives, promotions, advertising
campaigns, pricing, etc.
 Offering product or services with
counterseasonal demand
patterns (counterseasonal product mixing)
 Backordering
 Creation of new demand
 Partnering with suppliers to reduce information
distortion along the supply chain
Options of Adjusting Capacity to Meet
Demand (1 of 2)
Producing at a constant rate and using inventories
to absorb fluctuations in demand ie. changing
inventory levels
Varying work force size (hiring and firing workers)
so that production matches demand
Varying production capacity by increasing or
decreasing working hours (overtime or idle time)
Options of Adjusting Capacity to Meet
Demand (2 of 2)
Using part-time workers to change production rate
Subcontracting work to other firms
Providing the service or product at a later time
period (backordering)
Strategy Details
 Overtime & undertime - common when
demand fluctuations are not extreme
 Subcontracting - useful if supplier meets
quality & time requirements
 Part-time workers - feasible for unskilled
jobs or if labor pool exists
 Backordering - only works if customer is
willing to wait for product/services
Capacity Options - Advantages and
Disadvantages (1 of 4)
Option
Advantage
Disadvantage
Some
Comments
Changing
inventory levels
Changes in
human resources
are gradual, not
abrupt
production
changes
Inventory
holding costs;
Shortages may
result in lost
sales
Applies mainly
to production,
not service,
operations
Varying
workforce size
by hiring or
layoffs
Avoids use of
other alternatives
Hiring, layoff,
and training
costs
Used where size
of labor pool is
large
Advantages/Disadvantages (2 of 4)
Option
Advantage
Disadvantage
Some
Comments
Varying
production rates
through overtime
or idle time
Matches seasonal
fluctuations
without
hiring/training
costs
Permits
flexibility and
smoothing of the
firm's output
Overtime
premiums, tired
workers, may not
meet demand
Allows
flexibility within
the aggregate
plan
Loss of quality
control; reduced
profits; loss of
future business
Applies mainly
in production
settings
Subcontracting
Advantages/Disadvantages (3 of 4)
Option
Advantage
Disadvantage
Some
Comments
Using part-time
workers
Less costly and
more flexible
than full-time
workers
Good for
unskilled jobs in
areas with large
temporary labor
pools
Influencing
demand
Tries to use
excess capacity.
Discounts draw
new customers.
High
turnover/training
costs; quality
suffers;
scheduling
difficult
Uncertainty in
demand. Hard to
match demand to
supply exactly.
Creates
marketing ideas.
Overbooking
used in some
businesses.
Advantages/Disadvantages
(4 of 4)
Option
Advantage
Disadvantage
Some
Comments
Back ordering
during highdemand periods
May avoid
Customer must
overtime. Keeps be willing to
capacity constant wait, but
goodwill is lost.
Many companies
backorder.
Counterseasonal Fully utilizes
May require
products and
resources; allows skills or
service mixing
stable workforce. equipment
outside a firm's
areas of
expertise.
Risky finding
products or
services with
opposite demand
patterns.
The Extremes
Level
Strategy
Chase
Strategy
Production rate
is constant
Production
equals
demand
Basic Aggregate Planning Strategies
for Meeting Demand
Level capacity strategy:
• Keeping work force constant and maintaining a steady
rate of regular-time output while meeting variations in
demand by a combination of options (such as using
inventories + subcontracting)
Chase demand strategy:
• Changing workforce levels so that production matches
demand (the planned output for a period is set at the
expected demand for that period.)
Maintaining resources for high demand levels
• Ensures high levels of customer service
Level Production
Demand
Units
Production
Time
Chase Demand
Demand
Units
Production
Time
Level Strategy: Forecast and
Average Forecast Demand
Production rate per working day
70
60
50
Forecast
Demand
Level production using
average monthly
forecast demand
40
30
20
10
0
Jan
Feb
Mar
Apr
May
Jun
22
18
21
21
22
20
Level Strategy: Cumulative
Demand Graph
Cumulative Demand (Units)
7,000
6,000
Reduction of
inventory
Cumulative level
5,000 production using
4,000 average monthly
forecast
3,000 requirements
2,000
1,000
Cumulative forecast
requirements
Excess inventory
Jan Feb Mar Apr May Jun
Level Approach
• Advantages
– Stable output rates and workforce
• Disadvantages
– Greater inventory costs
– Increased overtime and idle time
– Resource utilizations vary over time
Chase Approach
• Advantages
– Investment in inventory is low
– Labor utilization in high
• Disadvantages
– The cost of adjusting output rates and/or
workforce levels
Aggregate Planning Methods
Graphical & charting techniques
• Popular & easy-to-understand
• Trial & error approach
Mathematical approaches
•
•
•
•
•
•
Linear programming
Transportation method
Linear decision rule (LDR)
Search decision rule (SDR)
Management coefficients model
Simulation
Summary of Planning Techniques
Technique
Solution
Characteristics
Graphical/charting
Trial and
error
Linear
programming
Linear
decision rule
Optimizing
Simulation
Trial and
error
Intuitively appealing, easy to
understand; solution not
necessarily optimal.
Computerized; linear
assumptions not always valid.
Complex, requires considerable
effort to obtain pertinent cost
information and to construct
model; cost assumptions not
always valid.
Computerized models can be
examined under a variety of
conditions.
Optimizing
Steps of Trial & Error Method
1. Forecast demand for each period
2. Determine capacities (for regular time, overtime,
subcontracting) for each period
3. Identify policies that are pertinent
4. Determine costs (labor, hiring/firing, holding etc.)
5. Develop alternative plans and costs
6. Select the best plan that satisfies objectives.
Otherwise return to step 5.
Aggregate Planning Using Pure
Strategies
(Example 1)
QUARTER
Spring
Summer
Fall
Winter
Hiring cost
Firing cost
Inventory carrying cost
Production per employee
Beginning work force
SALES FORECAST (LB)
80,000
50,000
120,000
150,000
= $100 per worker
= $500 per worker
= $0.50 pound per quarter
= 1,000 pounds per quarter
= 100 workers
Level Production Strategy
(1 of 2)
QUARTER
SALES FORECAST (LB)
Spring
Summer
Fall
Winter
80,000
50,000
120,000
150,000
Level production
(50,000 + 120,000 + 150,000 + 80,000)
4
= 100,000 pounds
Level Production Strategy
(2 of 2)
QUARTER
Spring
Summer
Fall
Winter
SALES
FORECAST
80,000
50,000
120,000
150,000
Total
PRODUCTION
PLAN
INVENTORY
100,000
100,000
100,000
100,000
400,000
20,000
70,000
50,000
0
140,000
Cost = 140,000 pounds x 0.50 per pound = $70,000
Chase Demand Strategy
QUARTER
SALES PRODUCTION
FORECAST
PLAN
Spring
Summer
Fall
Winter
80,000
50,000
120,000
150,000
80,000
50,000
120,000
150,000
WORKERS
NEEDED
80
50
120
150
WORKERS WORKERS
HIRED
FIRED
0
0
70
30
20
30
0
0
100
50
Cost = (100 workers hired x $100) + (50 workers fired x $500)
= $10,000 + 25,000 = $35,000
APP Using Mixed Strategies
MONTH
January
February
March
April
May
June
DEMAND (CASES)
1000
400
400
400
400
400
MONTH
July
August
September
October
November
December
DEMAND (CASES)
500
500
1000
1500
2500
3000
Production per employee = 100 cases per month
Wage rate = $10 per case for regular production
= $15 per case for overtime
= $25 for subcontracting
Hiring cost = $1000 per worker
Firing cost = $500 per worker
Inventory carrying cost = $1.00 case per month
Beginning work force = 10 workers
Aggregate Planning
(Example 2)
Suppose we have the following unit
demand and cost information:
Demand/mo
Jan
Feb
Mar
Apr
May
Jun
4500
5500
7000
10000
8000
6000
Materials
Holding costs
Marginal cost of stockout
Hiring and training cost
Layoff costs
Labor hours required
Straight time labor cost
Beginning inventory
Productive hours/worker/day
Paid straight hrs/day
$5/unit
$1/unit per mo.
$1.25/unit per mo.
$200/worker
$250/worker
0.15 hrs/unit
$8/hour
250 units
7.25
8
Cut-and-Try Example: Determining
Straight Labor Costs and Output
Given the demand and cost information below, what
are the aggregate hours/worker/month, units/worker, and
dollars/worker?
Demand/mo
Jan
Feb
Mar
Apr
May Jun
4500
5500
7000
10000
8000 6000
7.25x22
7.25/0.15=48.33 &
48.33x22=1063.33
22x8hrsx$8=$1408
Days/mo
Hrs/worker/mo
Units/worker
$/worker
Jan
22
159.5
1063.33
$1,408
Feb
19
137.75
918.33
1,216
Mar
21
152.25
1015
1,344
Apr
21
152.25
1015
1,344
May
22
159.5
1063.33
1,408
Jun
20
145
966.67
1,280
Chase Strategy
(Hiring & Firing to meet demand)
Days/m o
Hrs/wo rker/m o
Units/wo rker
$ /wo rker
Dem and
Beg. inv.
Net req.
Req. wo rkers
Hired
Fired
W o rkfo rce
Ending invento ry
Jan
22
1 5 9 .5
1 ,0 6 3 .3 3
$ 1 ,4 0 8
Jan
4 ,5 0 0
250
4 ,2 5 0
3 .9 9 7
3
4
0
Lets assume our current workforce is 7
workers.
First, calculate net requirements for
production, or 4500-250=4250 units
Then, calculate number of workers
needed to produce the net
requirements, or
4250/1063.33=3.997 or 4 workers
Finally, determine the number of
workers to hire/fire. In this case we
only need 4 workers, we have 7, so
3 can be fired.
Below are the complete calculations for the remaining
months in the six month planning horizon
Days/mo
Hrs/worker/mo
Units/worker
$/worker
Demand
Beg. inv.
Net req.
Req. workers
Hired
Fired
Workforce
Ending inventory
Jan
22
159.5
1,063
$1,408
Feb
19
137.75
918
1,216
Mar
21
152.25
1,015
1,344
Apr
21
152.25
1,015
1,344
May
22
159.5
1,063
1,408
Jun
20
145
967
1,280
Jan
4,500
250
4,250
3.997
Feb
5,500
Mar
7,000
Apr
10,000
May
8,000
Jun
6,000
5,500
5.989
2
7,000
6.897
1
10,000
9.852
3
8,000
7.524
6,000
6.207
2
8
0
1
7
0
3
4
0
6
0
7
0
10
0
Below are the complete calculations for the remaining months in
the six month planning horizon with the other costs included
Demand
Beg. inv.
Net req.
Req. workers
Hired
Fired
W orkforce
Ending inventory
Material
Labor
Hiring cost
Firing cost
Jan
4,500
250
4,250
3.997
3
4
0
Feb
5,500
Mar
7,000
Apr
10,000
May
8,000
Jun
6,000
5,500
5.989
2
7,000
6.897
1
10,000
9.852
3
8,000
7.524
6,000
6.207
2
8
0
1
7
0
6
0
7
0
10
0
Jan
Feb
Mar
Apr
May
Jun
$21,250.00 $27,500.00 $35,000.00 $50,000.00 $40,000.00 $30,000.00
5,627.59
7,282.76
9,268.97 13,241.38 10,593.10
7,944.83
400.00
200.00
600.00
750.00
500.00
250.00
Costs
203,750.00
53,958.62
1,200.00
1,500.00
$260,408.62
Level Workforce Strategy
(Surplus and Shortage Allowed)
Lets take the same problem as
before but this time use the
Level Workforce strategy
This time we will seek to use
a workforce level of 6 workers
Demand
Beg. inv.
Net req.
W orkers
P roduction
Ending inventory
Surplus
Shortage
Jan
4,500
250
4,250
6
6,380
2,130
2,130
Below are the complete calculations for the remaining
months in the six month planning horizon
Demand
Beg. inv.
Net req.
Workers
Production
Ending inventory
Surplus
Shortage
Jan
4,500
250
4,250
6
6,380
2,130
2,130
Feb
5,500
2,130
3,370
6
5,510
2,140
2,140
Mar
7,000
2,140
4,860
6
6,090
1,230
1,230
Apr
10,000
1,230
8,770
6
6,090
-2,680
May
8,000
-2,680
10,680
6
6,380
-1,300
Jun
6,000
-1,300
7,300
6
5,800
-1,500
2,680
1,300
1,500
Note, if we recalculate this sheet with 7 workers
we would have a surplus
Below are the complete calculations for the
remaining months in the six month planning
horizon with the other costs included
Jan
4,500
250
4,250
6
6,380
2,130
2,130
Jan
$8,448
31,900
2,130
Feb
5,500
2,130
3,370
6
5,510
2,140
2,140
Feb
$7,296
27,550
2,140
Mar
7,000
10
4,860
6
6,090
1,230
1,230
Mar
$8,064
30,450
1,230
Apr
10,000
-910
8,770
6
6,090
-2,680
May
8,000
-3,910
10,680
6
6,380
-1,300
Jun
6,000
-1,620
7,300
6
5,800
-1,500
2,680
1,300
1,500
Apr
$8,064
30,450
May
$8,448
31,900
Jun
$7,680
29,000
3,350
1,625
1,875
Note, total
costs under
this strategy
are less than
Chase at
$260.408.62
$48,000.00
181,250.00
5,500.00
6,850.00
$241,600.00
Labor
Material
Storage
Stockout
APP by Linear Programming
Minimize Z = $100 (H1 + H2 + H3 + H4)
+ $500 (F1 + F2 + F3 + F4)
+ $0.50 (I1 + I2 + I3 + I4)
Subject to
Demand
constraints
where
Ht = # hired for period t
Ft = # fired for period t
It = inventory at end
of period t
Pt = units produced
in period t
Wt = workforce size
for period t
Production
constraints
Work force
constraints
P1 - I1
I1 + P2 - I2
I2 + P3 - I3
I3 + P4 - I4
1000 W1
1000 W2
1000 W3
1000 W4
100 + H1 - F1
W1 + H2 - F2
W2 + H3 - F3
W3 + H4 - F4
= 80,000
= 50,000
= 120,000
= 150,000
= P1
= P2
= P3
= P4
= W1
= W2
= W3
= W4
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
APP by the Transportation
Method
QUARTER
EXPECTED
DEMAND
REGULAR
CAPACITY
OVERTIME
CAPACITY
SUBCONTRACT
CAPACITY
1
2
3
4
900
1500
1600
3000
1000
1200
1300
1300
100
150
200
200
500
500
500
500
Regular production cost per unit
Overtime production cost per unit
Subcontracting cost per unit
Inventory holding cost per unit per period
Beginning inventory
$20
$25
$28
$3
300 units
The Transportation Tableau
PERIOD OF USE
PERIOD OF PRODUCTION
1
Beginning
1
2
2
0
Inventory
300
Regular
600
3
—
20
300
6
—
23
100
29
1000
100
34
100
37
500
Subcontract
28
31
34
Subcontract
Regular
23
—
26
1200
25
28
150
31
150
28
31
—
1300
Overtime
200
Regular
250
—
23
25
—
28
500
1300
Overtime
200
Subcontract
500
Demand
900
1500
1600
34
20
28
Subcontract
4
—
31
20
300
26
28
1200
Capacity
9
—
25
Regular
Unused
Capacity
4
Overtime
Overtime
3
3
3000
250
500
1300
200
31
500
20
1300
25
200
28
500
250
50
Burruss’ Production
Plan
REGULAR
SUBENDING
PERIOD DEMAND PRODUCTION OVERTIME CONTRACT INVENTORY
1
2
3
4
Total
900
1500
1600
3000
7000
1000
1200
1300
1300
4800
100
150
200
200
650
0
250
500
500
1250
500
600
1000
0
2100
©The McGraw-Hill Companies, Inc., 2004
51
Other Quantitative Techniques
 Linear decision rule (LDR)
 Search decision rule (SDR)
 Management coefficients model
©The McGraw-Hill Companies, Inc., 2004
Hierarchical Planning Process
Production
Planning
Capacity
Planning
Resource
Level
Product lines
or families
Aggregate
production
plan
Resource
requirements
plan
Plants
Individual
products
Master
production
schedule
Rough-cut
capacity
plan
Critical
work
centers
Components
Material
requirements
plan
Capacity
requirements
plan
All
work
centers
Manufacturing
operations
Shop
floor
schedule
Input/
output
control
Individual
machines
Items
Aggregate Plan to Master Schedule
Aggregate
Planning
Disaggregation
Master
Schedule
Disaggregating the Aggregate Plan
• Master schedule: The result of disaggregating
an aggregate plan; shows quantity and timing
of specific end items needed to meet demand
for a scheduled horizon.
• Rough-cut capacity planning: Approximate
balancing of capacity and demand to test the
feasibility of a master schedule.
55
Figure 13.6
Master Scheduling Process
Inputs
Outputs
Beginning inventory
Forecast
Customer orders
Projected inventory
Master
Scheduling
Master production schedule
Uncommitted inventory
©The McGraw-Hill Companies, Inc., 2004
56
Projected On-hand Inventory
Projected on-hand
=
inventory
Inventory from
previous week
-
Current week’s
requirements
©The McGraw-Hill Companies, Inc., 2004
57
Projected On-hand Inventory
Figure 13.8
Beginning
Inventory
64
Forecast
Customer Orders
(committed)
Projected on-hand
inventory
Customer orders are
larger than forecast in
week 1
1
30
JUNE
2
3
30 30
4
30
5
40
33
20
10
4
2
31
1
-29
JULY
6
7
40 40
8
40
Forecast is larger than
Customer orders in week 3
Forecast is larger than
Customer orders in week 2
©The McGraw-Hill Companies, Inc., 2004
58
Time Fences
Time Fences – points in time
that separate phases of a
master schedule planning
horizon.
©The McGraw-Hill Companies, Inc., 2004
59
Time Fences in MPS
Figure 13.12
Period
1
2
“frozen”
(firm or
fixed)
3
4
5
“slushy”
somewhat
firm
6
7
8
9
“liquid”
(open)
©The McGraw-Hill Companies, Inc., 2004
Available-to-Promise
ON-HAND = 50
Forecast
Customer orders
Master production schedule
Available to promise
ON-HAND = 50
Forecast
Customer orders
Master production schedule
Available to promise
1
2
100
100
200
PERIOD
3
4
100
100
200
1
2
100
90
200
40
100
120
6
100
100
200
PERIOD
3
4
100
130
200
0
5
100
70
ATP in period 1 = (50 + 200) - (90 + 120) = 40
ATP in period 3 = 200 - (130 + 70) = 0
ATP in period 5 = 200 - (20 + 10) = 170
5
6
100
20
200
170
100
10
Available-to-Promise
Product
Request
Yes
Is the product
available at
this location?
No
Availableto-promise
Yes
Is an alternative
product available
at this location?
No
Allocate
inventory
Yes
Is this product
available at a
different
location?
No
Is an alternative
product available
at an alternate
location?
Yes
No
Allocate
inventory
Capable-topromise date
Is the customer
willing to wait for
the product?
No
Lose sale
Availableto-promise
Yes
Revise master
schedule
Trigger production
Aggregate Planning for Services
Most services can’t be inventoried
Demand for services is difficult to predict
Capacity availability is also difficult to predict
Service capacity must be provided at the
appropriate place and time
5. Labor is usually the most constraining resource
for services
6. Labor flexibility can be an advantage in services
1.
2.
3.
4.
Characteristics That Make Yield
Management Work
Service or product can be sold in advance of
consumption
Demand fluctuates
Capacity is relatively fixed
Demand can be segmented
Variable costs are low and fixed costs are
high
Hotel: Single Price Level
Sales
Demand Curve
$sales = Net price
* 50 rooms
=150*50
=$7500
Potential customers exist who are willing
to pay more than the $15 variable cost
Passed up
Some customers who
profit
paid $150 for the room
contributions
were actually willing to
pay more
Money left
on the table
$15 variable cost
of room
$150 Price
charged for room
$ Sales = $ 6,750
Price
Hotel: Two Price Levels
Sales
Net prices are:
Price #1 => $85
Price #2 => $175
Demand
Total sales =
1st net price *30 +
2nd net price *30
= $8100
$15 variable
cost of room
$100
Price #1
$Sales = $ 8,100
$200
Price #2
Yield Management
Cu
P(n < x) 
Cu + Co
where
n = number of no-shows
x = number of rooms or seats overbooked
Cu = cost of underbooking; i.e., lost sale
Co = cost of overbooking; i.e., replacement cost
P = probability
Yield Management
NO-SHOWS
PROBABILITY
0
1
2
3
.15
.25
.30
.30
Yield Management
NO-SHOWS
PROBABILITY
P(N < X)
0
1
2
3
.15
.25
.30
.30
.00
.15
.40
.70
Expected number of no shows
0(.15) + 1(.25) + 2(.30) + 3(.30) = 1.75
Optimal probability of no-shows
Cu
75
P(n < x)  C + C =
= .517
75
+
70
u
o
.517
Yield Management
NO-SHOWS
PROBABILITY
P(N < X)
Cost of overbooking
0
.15
.00
[2(.15) + 1(.25)]$70
= $38.50 Cost
1
.25 of bumping customers
.15
2(.30)$75 = $22.50 Lost
.30 revenue from no-shows
.40
.517
3
.30 cost of overbooking
.70
$61.00 Total
by
2 rooms
Expected number of no shows
Expected savings = ($131.225 - $61) = $70.25 a night
0(.15) + 1(.25) + 2(.30) + 3(.30) = 1.75
Optimal probability of no-shows
Cu
75
P(n < x)  C + C =
= .517
75 + 70
u
o