:
: ;
, ;
;
.
;
5.1. :
) TR = 9Q;
) MR = 3;
) TR = 8Q ¼ Q²;
) MR = 7 0,5Q.
.
:
, , . , . , , .
, (Q(D) = b aP), : (P=b / Q / a).
:
) TR = 9×Q; => P×Q = 9×Q; P=9.
) MR = 3; TR = 3×Q P×Q = 3Q; => P=3.
) TR = 8Q - ¼Q²; P×Q = 8Q - ¼Q²; => P = 8 ¼Q.
) MR = 7 - ½Q; TR = 7Q - ¼Q² P×Q = 7Q - ¼Q²; =>
P = 7- ¼Q.
: ); ) - , .. ; ); ) - , .. .
5.2. , MR = 60 2Q. : MC= -15 + 3Q.
.
. , .. , .
:
P = AR = TR / Q,
Q , .
, , .
:
(MR = MC) : 60 2Q = - 15 + 3Q. , (Q) 15.
(MR) , : TR = 60Q Q². , , , : TR = 60 × 15 15² = 675.
, P = AR = TR/Q = 675: 15 = 45.
|
|
: P = 45.
5.3. , , , :
P = 52 2Q. : TC = 120 8Q + Q².
:
(L):
(P MC) / P = 1 / |Ed|.
. , , , .
:
) , , MR = MC.
MR = (TR) = (P×Q)=((52 2Q) × Q)' = (52Q 2Q²)' = 52 4Q;
MC = (TC) = (120 8Q + Q²)' = 2Q 8.
MR MC. : 52 4Q = 2Q 8. , , , 10 .
) , , (AR).
: AR = TR / Q, TR = 52Q 2Q², Q = 10.
, :
AR = 32 .. (52Q 2 Q²) / Q = 52 2Q = 52 - 2 × 10).
(P) 32 (.. AR = 32).
) MC = 2Q 8 , . : MC = 2 × 10 8 = 12.
) (L):
(P MC) / P = 1 / |Ed|.
(32 12) / 32 = 1 / |Ed|
1,6 = 1 / |Ed| ==>
Ed = 1,6.
:
, . , , .
) P = 52 2Q. , (Q), . PR = TR TC, TR = P × Q. , , .
:
PR = (52 2Q) × Q (120 - 8Q + Q²) = 52Q 2 Q² (120 - 8Q + Q²) =>
PR = 60Q 3Q² 120.
, :
(PR)' = (60Q 3Q² 120)' = 60 6Q.
60 6Q = 0;
Q = 10.
, P = 52 2 ×10 = 32 ..
) .
: MC = (TC) = (120 8Q + Q²)' = 2Q 8. , , , MC = 2Q 8 = 2×10 8 = 12.
) Ed : (P MC) / P = 1 / |Ed|.
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(32 12) / 32 = 1 / |Ed|;
20 / 32 = 1/ |Ed|;
Ed = 1,6.
: Ed = 1,6. , .
5.4. , P = 25 Q = 100.
.
:
, Q(D) = b aP, :
(P), (/2 )
, (/2) (. 4.3 . 4.5).
) , :
Q(D) = b aP.
P = 0 Q(D) = = b ( ). , , Q = B/2 = b / 2. , , , : 100 = b / 2. b = 200.
Q(D) = 0 P = A = b/a ( ). , , P = A / 2 = b / 2a. , , : 25 = 200 / 2a. , = 4.
) : Q(D) = b aP. : Q(D) = 200 4P.
: Q(D) = 200 4P.
5.5. P(Q) = 40 bQ. : = 20. , .
:
, P = AR = TR / Q. TR = (40 - bQ) × Q = 40Q - bQ². P = (40Q - bQ²) / Q = 40 - bQ.
, , MC = MR. . MR, . MR = (TR)' = (40Q bQ²)' = 40 - 2 bQ.
MC MR, , . , 40 - 2bQ = 20, Q = 10 / b.
: P = 40 - bQ Q = 10 / b. P = 30.
: 30.