Answer to Question #332644 in Calculus for Olga

Question #332644

A firm has the following total and cost functions:

TR=20Q−4Q^2

TC=16−Q^2,


where Q is the number of unites produced and sold (in thousands). How many units should be produced to maximise the profit?


a.3,3333,333 units.


b.1,7141,714 units.


c.1,3331,333 units.


d.3 3333 333 units.



1
Expert's answer
2022-04-26T04:22:14-0400

Profit = TR - TC = 20Q - 4Q2 - (16 - Q2) = 20Q - 4Q2 - 16+ Q2 = 20Q-16- 3Q2

Profit has maximum, then

dProfitdQ=2032Q=0Q=20/6=3.3333Answer:a\frac{d Profit}{d Q} = 20 - 3*2*Q = 0\\ Q=20/6=3.3333\\ Answer:a

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