Question

1) There is a chemical factory that produces A ton of chemical products every day. The production cost of the known chemical is $\left(\frac{1}{2}A^2 - 50A + 50\right)$ per ton. and the selling price of the chemical is $\left(80 + \frac{1}{4}A\right)$ per ton. (i) What is the daily ton A of chemicals produced by the chemical plant to maximize its daily profit P? (Note: It is not necessary to verify the reasonable stagnation point of the first order derivative, let this stagnation point make the profit P the maximum value) (ii) What is the highest daily profit P?

          1) There is a chemical factory that produces A ton of chemical products every day.
The production cost of the known chemical is $\left(\frac{1}{2}A^2 - 50A + 50\right)$ per ton.
and the selling price of the chemical is $\left(80 + \frac{1}{4}A\right)$ per ton.
(i) What is the daily ton A of chemicals produced by the chemical plant to maximize its daily profit P?
(Note: It is not necessary to verify the reasonable stagnation point of the first order derivative, let this stagnation point make the profit P the maximum value)
(ii) What is the highest daily profit P?

1) There is a chemical factory that produces A ton of chemical products every day.
The production cost of the known chemical is ((1)/(2)A^2 - 50A + 50) per ton.
and the selling price of the chemical is (80 + (1)/(4)A) per ton.
(i) What is the daily ton A of chemicals produced by the chemical plant to maximize its daily profit P?
(Note: It is not necessary to verify the reasonable stagnation point of the first order derivative, let this stagnation point make the profit P the maximum value)
(ii) What is the highest daily profit P?

Added by Andr-S T.

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