Combining functions: Revenue, Cost, and Profit The revenue, cost, and profit for a product, each in...
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Combining functions: Revenue, Cost, and Profit 60 0.015 Rx x x 600 9 C x x x 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 R(x) 0 16,65030,60041,85050,40056,25059,40059,85057,60052,65045,000 x 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 C(x) 600 3,300 6,000 8,700 11,40014,10016,80019,50022,20024,90027,600 x 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 P(x) -600 13,35024,60033,15039,00042,15042,60040,35035,40027,75017,400 Px Rx C x The revenue, cost, and profit for a product, each in terms of dollars for sales of x units, are given below: Revenue Cost Profit Px R C x We can refer to the function P as the difference of functions R and C
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Transcript of Combining functions: Revenue, Cost, and Profit The revenue, cost, and profit for a product, each in...
Combining functions: Revenue, Cost, and Profit
60 0.015R x x x
600 9C x x
x 0 300 600 900 1200 1500 1800 2100 2400 2700 3000R(x) 0 16,650 30,600 41,850 50,400 56,250 59,400 59,850 57,600 52,650 45,000
x 0 300 600 900 1200 1500 1800 2100 2400 2700 3000C(x) 600 3,300 6,000 8,700 11,400 14,100 16,800 19,500 22,200 24,900 27,600
x 0 300 600 900 1200 1500 1800 2100 2400 2700 3000P(x) -600 13,350 24,600 33,150 39,000 42,150 42,600 40,350 35,400 27,750 17,400
P x R x C x
The revenue, cost, and profit for a product, each in terms of dollars for sales of x units, are given below:
Revenue
Cost
Profit
P x R C x We can refer to the function P as the difference of functions R and C
It can also be seen from the graph that profit is the difference of revenue and cost
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0 500 1,000 1,500 2,000 2,500 3,000
revenue - costprofit
Revenue
Cost
Profit
Composition of functions: Evaporation rate
Temperature 60 62 65 68 70 72 75 78 80 83 85 88 90
Evaporation rate (L/min) 2.1 2.6 3.5 4.7 5.7 7.0 9.4 12.7 15.5 20.9 25.6 34.5 42.2
Expected temperature T(h) for August 24 is a function of hour of day:
Evaporation rate E(T) of a small lake is a function of outside temperature:
Define evaporation rate as a function of hour of day:
E h E T h We can refer to the function P as the composition of functions E and T
Hour of day 10:00 11:00 12:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00
Temperature 60 62 68 75 83 88 90 88 83 75 68 62
Hour of day 10:00 11:00 12:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00
Evaporation rate (L/min)
What do you expect the
evaporation rate to be at 2:00?
Summary of combinations of functions
Name Notation Meaning
Sum of f and g
Difference of f and g
Product of f and g
Quotient of f and g
Composition of f and g
f g x
fg x
fx
g
f g x
f x g x
f g x f x g x
f x g x
, 0f x
g xg x
f g x
