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Sagot :
Assume the demand Q(P) is a linear function.
Q(390) = 1700
The slope = -200 /20 (The slope - demand line is always negative)
=-10
The point slope form of the equation is
Q - 1700 = -10 (P - 390)
Open the parenthesis
Q - 1700 = -10p + 3900
Q = -10p + 3900 + 1700
Q = -10p + 5600
Now solve for P
Q + 10P = 5600
10P = -Q + 5600
Divide through by 10
P = -1/10 Q + 560
Substitute Q = x
[tex]P(X)=-\frac{1}{10}x\text{ + 560}[/tex]The above is the demand function (price p as a function of units sold x).
a) The revenue function is defined as ;
R(P) = P * Q(P)
= p ( -10p + 5600)
= -10p² + 5600P
To maximaize the revenue,
Differentiate the above
R'(P) = -20P + 5600
Set R'(P)=0
-20P + 5600 =0
20P = 5600
Divide both-side by 20
P = 280
Hence, to maximize they should offer $280 to the buyers.
C)
C(x) is the cost to produce x television sets
C(Q(p)) is the cost to produce the demanded quantity
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