Question 58012: Kindly assist me with the following calculus problems :
Q1
calculation mad easy ltd , wishes to estblish its profit function . however the cost and revenue functions are not readily available and therefore need to be established first . the following data complied from past records for this purpose
units (x) 50 100 150 250 300
cost C(x) usd (000) 4250 5100 5950 7650 8500
revenue ( R) usd ( 000 ) 1700 3400 5100 8500 10200
a) determine the cost , revenue an profit function
b) find the break even piont
c) what is the ecpected profit when 400 units are produced and sold ?
Q2
market survey of suppliers of a particular product have resulted in the conclusion that the supply is approximately quadratic . suppliers were asked what quantities they would be willing to supply at different market prices .
the results of the survey are below
price ( usd) 25 30 40
supply (000) units 112.5 250 600
further survey of the demand pattern of the product indicated that the demand function was D(p)=p^2-100p-2500
a) determine the supply function
b) determine the market equilibrium price and quantity
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Q1
calculation mad easy ltd , wishes to estblish its profit function . however the cost and revenue functions are not readily available and therefore need to be established first . the following data complied from past records for this purpose
units (x) 50 100 150 250 300
cost C(x) usd (000) 4250 5100 5950 7650 8500
revenue ( R) usd ( 000 ) 1700 3400 5100 8500 10200
a) determine the cost , revenue an profit function
Cost:
Notice that when units increases by 50 the cost increases by 850;
so the cost function is linear. Pick two points to determine the
equation: (50,4250) (100,5100)
slope = 850/50=17
To find "b" 4250=(17)50+b; b=3400
C(x)=(17)x+3400
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Revenue:
The procedure is the same as with the cost.
R(x)=34x
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Profit equals Revenue - Cost
P(x)= 34x-(17x+3400) = 17x-3400
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b) find the break even point
C(x)=R(x)
17x+3400=34x
17x=3400
x=200
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c) what is the expected profit when 400 units are produced and sold ?
P(x)= 17x-3400
P(400)=17(400)-3400
=3400
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Q2
market survey of suppliers of a particular product have resulted in the conclusion that the supply is approximately quadratic . suppliers were asked what quantities they would be willing to supply at different market prices .
the results of the survey are below
price ( usd) 25 30 40
supply (000) units 112.5 250 600
further survey of the demand pattern of the product indicated that the demand function was D(p)=p^2-100p-2500
a) determine the supply function
Using the Quadratic Regression function on a TI-83 calculator
I find that S(x)=(1/2)x^2-(1.6 * 10^-11)x-200
b) determine the market equilibrium price and quantity
I assume this means Supply equals Demand:
[(1/2)x^2-(1.6 * 10^-11)x-200]-(p^2-100p-2500)=0
-(1/2)x^2+100p+2400=0
x^2-200p-1200=0
x=[200+-sqrt(35200)]/2
x=387.62 or x=12.38
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Cheers,
Stan H.
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