Answer:
The solution and relevant data for the exercise are contained within three images. The maximum profit amounts to 262.500.
Explanation
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Answer:
A) The equation for net benefits is given by 20 + 24Q - 4Q²
B) 40; 40
C) MNB(Q) = 24 - 8Q
D) 16; -16
E) Q = 3
F) 0
Explanation:
a) This outlines the formula for net benefits.
Essentially, net benefits arise when total benefits surpass total costs from Q units of the control variable.
From this definition, we derive the equation
N(Q)= B(Q) - C(Q)
Where
N(Q)= Net benefits from Q units of control variable
B(Q)= Total benefits from Q control variable units
C(Q)= Total cost from Q units of the control variable
We are informed that B(Q)= 100 + 36Q - and C(Q) = 80 +12Q
This implies:
N(Q)= 100 + 36Q - 4Q² - (80 + 12Q)
= 100 + 36Q - 4Q² - 80 - 12Q
= 20 + 24Q - 4Q²
b) To find the net benefits when Q = 1 and Q=5
Step 1) For Q=1, we apply the 20 + 24Q - 4Q² formula
= 20 + 24(1) - 4(1²)
= 20 + 24 - 4
= 40
Step 2) For Q=5, we use the 20 + 24Q - 4Q² formula
= 20 + 24(5) - 4(5²)
= 20 + 120 - 100= 40
c) To determine the marginal net benefits equation
Marginal net benefits reflect the change in net benefits caused by a change of one unit in the control variable
The formula is formulated as follows:
MNB(Q) = MB (Q) - MC(Q)
Where
MNB(Q)= The marginal net benefits at the Q level of the control variable
MB(Q)= marginal benefits
MC(Q)=Marginal Costs
We are already informed: MB(Q) = 36 – 8Q and MC(Q) = 12.
This indicates
MNB(Q)=MB (Q)-MC(Q)
= 36-8Q-12
= 36-12-8Q
= 24-8Q
Thus, MNB(Q) = 24-8Q
d) To find marginal net benefits
Step 1) When Q=1 we apply the marginal net benefit formula MNB(Q)= 24-8Q
=MNB(Q)= 24-8(1)
= 16
Step 2) For Q=5 we utilize the marginal net benefit MNB(Q)= 24-8Q
=MNB(Q)= 24-8(5)
=24-40
=-16
e) To calculate maximum net benefits, which occur when marginal costs equal marginal benefits (indicating the control variable level).
MB(Q)=MC(C)
MB(Q)= Marginal benefits
MC(Q)= Marginal Costs
We know that MB(Q) =36-8Q and MC(Q)=12
Therefore, setting maximum benefit
= MB(Q)= MC(Q)
=36-8Q=12
8Q=36-12
8Q= 24
So, Q= 3.
This indicates that at Q equal to 3, net benefits achieve maximum levels
f) To compute marginal net benefits - the difference between marginal costs and benefits
MNB(Q)=MB(Q)-MC(Q)
MNB(Q)= Marginal net benefits
MB(Q)= Marginal benefits
MC(Q)= Marginal Costs
We are aware that MB(Q) =36-8Q and MC(Q)=12
MNB(Q)= 36-8Q-12
=36-12-8Q
=24-8Q
As established, maximum levels of net benefits occur at Q = 3, substituting Q with 3 in the equation
MNB(Q)= =24-8(3)
= 24-24
=0
This indicates that at Q = 3, net costs balance out with net benefits, maximizing net benefits.