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F5 – Performance Management
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Decision making
Questions
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Questions
• Dec 2007 Q4 (a)(b)
• June 2008 Q2 (a)(b) (c)
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Dec 2007 Q4 (a)
Outline the financial and other factors that Sniff Coshould consider when making a further processingdecision
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Answer
Following factors in any further processing decision
• Forecast sales level changes
• Incremental costs
• Incremental revenues
• Effect on customers
• Effect on reputation
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Dec 2007 Q4 (b)
Standard perfume $39.98 per 100ml
Consider adding hormone
Market research cost $3,000
1000lt to be further processed (10% of production)
99% is dilued alcohol costing $20/lt
Balance is oil costing $18,00/lt
Labour for 1000lts is 200 hrs @ $15/hr
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Dec 2007 Q4 (b)
200lt of the output will be for male customers
2lt of hormone costing $7,750 to be added
800lt will be for female customers with 8lt of hormoneadded costing $12,000/lt
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Dec 2007 Q4 (b)
Supervisor paid $35,00pa to be spend 10% of time onnew products (50/50)
Additional 500hrs needed to work on male versionand 700hrs on female version.
Labour currently working at full capacity.
F O/H allocated @ $25 per lab hr
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Dec 2007 Q4 (b)
Sales price for this one-off promotion are
• Male $75.00 per 100ml
• Female $59.50 per 100ml
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Dec 2007 Q4 (b)
Required
Provide a separate assessment and conclusion forthe male and the female versions of the product
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Answer
Calculate
• Additional revenue generated
Male & Female
• Additional costs incurred
Male & Female
If costs > revenue => do not produce
If costs < revnue => do produce
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Answer
Additional/Incremental revenue
Male
Original 200lt @ $399.80 79,960
Update 200lt + 2lt hormone
= 202lt @ $750/lt 151,500
Increase in revenue 71,540
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Answer
Additional/Incremental revenue
FemaleOriginal 800lt @ $399.80 319,840
Update 800lt + 8lt hormone
= 808lt @ $595/lt 480,760
Increase in revenue 160,920
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Answer
Additional/Incremental costs
• To make the updated product we need to take labourfrom production
• Must calculate the contribution that will be lost bytaking labour from production of the original product
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Answer
Contribution generated by original product (1000 litres)
Sales 1000 @ 399.80 399,800
Materials
Alcohol 990lt @ $20/lt (19,800)
Oil 10lt @ $18,000/lt (180,000)
Labour 2,000hr @ $15/hr (30,000)
Contribution 170,000
Contribution per hour potentially lost
170,000 / 2000 = $85/hr
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Answer
Incremental costs – Male
Labour
500hrs @ $15 7500
500hrs @ $85 42500Hormone
2lt @ $7750/lt 15500
Supervisor 0
O/Hs 0
Reasearch 0
Incremenatl costs 65,500
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Answer
Incremental costs – Female
Labour
700hrs @ $15 10500
700hrs @ $85 59500
Hormone
8lt @ $12000/lt 96000
Supervisor 0
O/Hs 0
Reasearch 0
Incremenatl costs 166,000
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Answer
Incremental profit
Male Female
Incremental rev 71,540 160,920
Incremental cost (65,500) (166,000)
Net benefit 6,040 (5,080)
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June 2008 Q2 (a)
Manufacture pool and snooker cues
Ash restricted to 5,400kg @ $40/kg
Labour limited to 12,000hrs @ $18/hr
Demand Price
Pool cues 15,000 $41
Snooker cues 12,000 $69
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June 2008 Q2 (a)
Standard cost cardPool Snooker
Labour/cue 0.5hr 0.75
Ash/cue 270g 270g
Other variable costs $1.20 $4.70
Calculate contribution per cue
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June 2008 Q2 (a) - answer
Contribution = Selling Price – Variable cost
Pool Snooker
Price 41.00 69.00
Lab @ $1/hr (9.00) (13.50)
Mat @ $40/g (10.80) (10.80)
Other (1.20) (4.70)
Contribution 20.00 40.00
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June 2008 Q2 (b)
Determine the optimal production plan for a typicalperiod assuming that HC is seeking to maximisethecontribution earned.
You should use a linear programming graph, identifythe feasible region and the optimal point andaccurately calculate the maximum contribution thatcould be earned using whichever equations youneed
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June 2008 Q2 (b) - answer
Step 1Assign symbols to unknown quantities.
Let pool cues = X
Let snooker cues = Y
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June 2008 Q2 (b) - answer
Step 2 Express the constraints.
Materials (kg)
.27x + .27y <= 5,400
Labour (hrs)
.5x +.75y <= 12,000
Demand
x <= 15,000 y <= 12,000
Non-negativity
x >= 0 y>= 0
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June 2008 Q2 (b) - answer
Step 3
Formulate the objective function.
Z = 20x + 40y
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June 2008 Q2 (b) - answer
Step 4
Solve the equations - graph each constraint
.27x + .27y <= 5 ,400 .5x +.75y <= 12,000
x = 0 x= 0
.27y = 5400 .75y = 12000
y = 20,000 y = 16000
y = 0 y = 0
.27x = 5400 .5x = 12000
x = 20,000 x = 24000
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June 2008 Q2 (b) - answer24
20
18 .27x + .27y <= 5,400
16
14
12
10 .5x +.75y <= 12,000
8
8 10 12 14 16 18 20 22 24
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June 2008 Q2 (b) - answer24
20
18 .27x + .27y <= 5,400
16
14
12
10 .5x +.75y <= 12,000
8
8 10 12 14 16 18 20 22 24
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June 2008 Q2 (b) - answer
Draw the ISO contribution line
Z = 20x + 40y
20x + 40y = 320
x = 0 y = 0
40y = 320 20x = 320
y = 8 x = 16
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June 2008 Q2 (b) - answer24
20
18 .27x + .27y <= 5,400
16
14
12
10 .5x +.75y <= 12,000
8
8 10 12 14 16 18 20 22 24
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June 2008 Q2 (b) - answer24
20
18 .27x + .27y <= 5,400
16 Optimal point
14
12
10 .5x +.75y <= 12,000
8
8 10 12 14 16 18 20 22 24
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June 2008 Q2 (b) - answer
Optimal point is intersection of
.5x +.75y <= 12,000 (labour)
y <= 12,000 (max demand)
Solve the equations
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June 2008 Q2 (b) - answer
.5x +.75y <= 12,000 (1))
y <= 12,000 (2)
Replace y in (1) with 12,000
.5x + .75 (12000) = 12000
.5x = 3000
x = 6000
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June 2008 Q2 (b) - answer
Optimal production mix is
6000 pool cues
12000 snooker cues
Contribution is
Z = 20x + 40y
= 20 (6000) + 40(12000)
= $600,000
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June 2008 Q2 (c)
Some of the craftsmen have offered to work overtime,provided that they are paid double time for theextra hours overthe contracted 12,000 hours.
HC has estimated that up to 1,200 hours per periodcould be gained in this way
Explain the meaning of a shadow price (dual price)and calculate the shadow price of both the labour(craftsmen) and the materials (ash)
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June 2008 Q2 (c) - answer
Shadow price is the additional value on having anaditional unit of a scarce resource available.
The value is usually the additional contributionearned. This si the maximum amount we would payfor having that additonal unit.
We have shown that material (ash) is not a limitingfactor in this problem so it has a zero shadow price
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June 2008 Q2 (c) - answer24
20
18 .27x + .27y <= 5,400
16 Optimal point
14
12
10 .5x +.75y <= 12,000
8
8 10 12 14 16 18 20 22 24
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June 2008 Q2 (c) - answer
Labour is limited so we can calculate a shadow price.
. 5x +.75y <= 12,001 ( 1))
y <= 12,000 (2)
Replace y in (1) with 12,000
.5x + .75 (12000) = 12001
.5x = 3001
x = 6002
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June 2008 Q2 (c) - answer
Optimal production mix is
6002 pool cues
12000 snooker cues
Contribution is
Z = 20x + 40y
= 20 (6002) + 40(12000)
= $600,040
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June 2008 Q2 (c) - answer
Original contribution – New contribution
= Shadow price
Original 600,000
New 600,040
Shadow price 40
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End of question session
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