1-Given the following functions: TR\\left(Q\ ight)=-4Q^2+24Q-120 T R ( Q ) = 4 Q
ID: 1134025 • Letter: 1
Question
1-Given the following functions: TRleft(Q ight)=-4Q^2+24Q-120
T R ( Q ) = 4 Q 2 + 24 Q 120 TCleft(Q ight)=-3Q^2-24Q+300
T C ( Q ) = 3 Q 2 24 Q + 300
What is the quantity break-even point?
2-
Given the following functions:
What is the quantity which maximizes profits?
Given the following functions:
What is the quantity where profits go from positive to zero?
7-
Given the following functions:
What is the quantity where profits go from positive to zero?
Given the following functions:
What is the quantity where profits go from positive to zero?
3-
Explanation / Answer
1) we know that total profit at break even point is zero .
TR-TC = 0
4 Q2 + 24 Q 120 - ( 3 Q2 24 Q + 300) = 0
-4Q2 +24Q - 120 +3Q2 + 24Q - 300 = 0
-Q2 + 48Q = 420
-Q ( Q + 48) = 420
Q = -420 ( quantity never be in minus)
Q + 48 = 420
Q = 420 -48 = 372
so, the break even quantity is 372.
2) the quantity which maximizes profits at MR=MC
MR = -8Q +24
MC = -6Q - 24
-8Q + 24 = -6Q - 24
-2Q = -48
Q = 24
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