Which of the following will you see in a
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Answer:
The level of production x that will maximize the profit is: 22,966
Explanation:
C(x) = 50,000 + 100x + x³
R(x) = 3400x
P(x) = R(x) - C(x)
= 3400x - [50,000 + 100x + x³]
= 3400x - 50,000 - 100x - x³
= 3300x - 50,000 - x³ .................... (A)
P'(x) = 3300(1) - 0 - 3x²
= 3300 - 3x²
At a critical point, P'(x) = 0
∴ 0 = 3300 - 3x²
3x² = 3300
x² = 1100
x = ±
P"(x) = -6x
P() = -6 (
) < 0
by second derivative, 'P' max at x = = 33.17 (rounds)
since x = ,
recall that P(x) = 3300x - 50,000 - x³ from equation (A)
Therefore, Maximum Profit
P() = 3300
- 50000 -
= 3300(33.17) - 50,000 - 33.17³
= 109461 -50,000 - 36495.26
= 22,965.74
Maximum profit is 22,966 to the nearest whole number
It should be noted that in the PPC, the downward sloping line 'ab' is the production possibility curve.
<h3>How to illustrate the information?</h3>In the diagram, since point 'A' falls on the PPC itself, it represents the full employment of resources. Point 'A' represents the combination of 30 million bananas and 10 million robots.
Opportunity cost producing a robot = Total bananas possible / Total robots possible
Opportunity cost producing a robot =60/20
Opportunity cost producing a robot = 3 bananas
The area outside PPC represents the unattainable combinations of two goods.
During the recession, the resources are inefficiently used and the production combination is represented by point 'B' which falls below PPC When the production technology improves only for one good and not for the other, the PPC rotates
Marginal opportunity cost of a robot = 80 million bananas / 10 million robots
The marginal opportunity cost of a robot = 8 bananas
Opportunity cost of 2 million robots = 8 bananas × 2 million
The opportunity cost of 2 million robots will be 16 million bananas.
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